n = 480 (*n==8,48,480,5760,...*)

If[n == 8,
 Print["n=8"];
 v = {11, 2, 1, 8, 7, 14, 13, 4};
 penultimateValue = v[[n - 1]]; (*13*)
 constant1 = Total[v]; (*(60) sum of all the values*)
 constant2 =
  constant1/(n/2); (*(15) sum of pairwise differences (OEIS A060753)*)


 constant3 =
  7; (*absolute value of min value of pairwise differences, and also \
the first value minus last value, and also the sum of pairwise \
differences*)
 constant4 = 35; (*sum of absolute values of pairwise differences*)
 constant5 = 16;(*16=2 x 2 x 2 x 2*)
 constant6 = 9; (*max value of pairwise differences*)
 constant7 =
  1; (*value from the sequence 1,3,15,45,45,405,4455,... given by \
A005867(n-1)/2^A057773(n-1). used for constant8=constant1/constant7*)


 constant8 = constant1/constant7 (*(60)*)
 ]

If[n == 48,
 Print["n=48"];
 v = {27, -18, 1, 4, 23, 26, 13, 32, 19, 22, 41, 44, 31, 18, 37, 24,
   27, 46, 33, 36, 23, -6, -3, 16, 19, 38, 41, 12, -1, 2, -11, 8,
   11, -2, 17, 4, -9, -6, 13, 16, 3, 22, 9, 12, 31, 34, 53, 8};
 penultimateValue = v[[n - 1]]; (*53*)
 constant1 = Total[v]; (*(840)*)
 constant2 = constant1/(n/2); (*(35)*)
 constant3 = 19;
 constant4 = 641;
 constant5 = 192;(*192=2 x 2 x 2 x 2 x 2 x 2 x 3*)
 constant6 = 45;
 constant7 = 3;
 constant8 = constant1/constant7 (*(280)*)
 ]

If[n == 480,
 Print["n=480"];
 v = {61, -54, -41, 4, 17, -2, 43, 24, 37, 82, 95, 76, 57, 102, 83,
   96, 141, 122, 135, 116, 65, 78, 123, 136, 181, 194, 47, 60, 41, 86,
    3, 48, 29, 10, 23, 68, 81, 62, 107, 24, 69, 82, 127,
   12, -71, -26, -13, 32, 45, 26, 71, 52, 65, 46, 27, 8, 53, 34, 47,
   92, 73, 86, 67, 16, 29, 74, 87, 68,
   17, -2, -85, -40, -27, -46, -1, -20, -39, -26, 19, 32, 13, 58, 39,
   52, 97, 78, -5, 40, -43, 2, 15, 60, 73, 54, 3, 16, 61, 74, -41,
   4, -15, -2, 43, 24, 37, 18, -97, -52, -39, 6,
   19, -32, -51, -38, -57, -12, 1, -18, 27, 8, -75, -30, -17, -36,
   9, -10, 3, 48, 61, 106, 23, 68, -15, 30, 43, 24, 5, 50, 31, 12, 25,
    6, -13, 32, 13, 26, 71, 52, 65, 46, -5, 8, 53, 34,
   47, -4, -23, -10, -29, 16, 29,
   10, -41, -60, -47, -2, -85, -40, -59, -46, -1, 12, 57, -26,
   19, -64, -19, -6, 39, 52, 1, -18, -5, 40, 53, 34, 15, 60, 41, 54,
   3, 16, -3, -54, -41, 4, 17, 62, 75, 24, 5, 18, -1, -20, -39,
   6, -13, -32, -19, 26, 39, 20, 65, 46, 59, 104, 117, 162, 79, 124,
   41, 86, 67, 80, 61, 106, 87, 100, 145, 158, 139, 120, 69, 82, 127,
   108, 25, -26, -13, 32, 45, 90, 103, 52, -31, -50, -5,
   8, -43, -62, -81, -68, -23, -10, -29, 16, -3, 10, -9,
   36, -47, -2, -85, -40, -27, 18, 31, 12, 57, 38, 51, 96, 109, 90,
   71, 116, 97, 78, 59, 72, 53, 2, 15, 60, 73, 118, 131, 80, 61, 74,
   23, 36, 17, 62, 43, 24, 37, 82, 95, 76, 25, 38, 83, 96, 141, 58,
   103, 20, 65, 78, 123, 136, 117, 162, 79, 124, 137, 118, 67, 48, 61,
    106, 87, 100, 81, 30, 43, 24, 69, 82, 31, 12, 25, 6, 51, 64, 45,
   90, 71, 52, 65, 46, 27, 72, 53, 34, 47, 92, 9, 54, -29, 16, 29, 74,
    87, 68, 113, 94, 107, 152, 69, 50, 95, 76, 89, 134, 115, 128, 109,
    58, 71, 116, 129, 174, 59, 40, 53, 34, 79, 92, 73, 118, 3, 16, 61,
    74, 23, 4, 17, 62, 75, 120, 37, 82, -1, -20, 25, 38, 19, 64, 45,
   58, 103, 116, 97, 78, 123, 104, 117, 162, 79, 60, 9, -10, 3, 48,
   61, 10, -9, 4, -15, 30, 43, 24, 69, 50, 31, 12, 25, 6, 51, 32, 45,
   90, 103, 148, 65, -50, -5, 8, 53, -30, 15, -4, 9, 54, 67, 48, 29,
   74, -9, 36, 17, 30, -117, -104, -59, -46, -1,
   12, -39, -58, -45, -64, -19, -6, -25, 20, 1, -18, -5, 40, 53, 34,
   79, 60, 73, 118, 131, 16};
 penultimateValue = v[[n - 1]]; (*131*)
 constant1 = Total[v]; (*(18480)*)
 constant2 = constant1/(n/2);(*(77)*)
 constant3 = 45;
 constant4 = 15615;
 constant5 =
  3840;(*3840=2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5, (3x5=15)*)
 constant6 = 147;
 constant7 = 15;
 constant8 = constant1/constant7(*(1232)*)
 ]

If[n == 5760,
 Print["n=5760"];
 v = {1, 2, 3, 4, 5}; (*add the correct 5760 values here later*)
 penultimateValue = v[[n - 1]]; (*2263*)
 constant1 = Total[v]; (*(2882880)*)
 constant2 = constant1/(n/2); (*(1001)*)
 constant3 = 617;
 constant4 = 2523883;
 constant5 =
  552960;(*552960=2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x \
3 x 3 x 5, (3x3x3x5=135)*)
 constant6 = 3223;
 constant7 = 45;
 constant8 = constant1/constant7(*(64064)*)
 ]


Total[Total[
   Table[v[[i]] - Sort[Table[v[[i]], {i, 1, n}]], {i, 1, n}]]] == 0
(*possibly always true*)

Abs[Total[Table[v[[i]], {i, 1, n/2}]] -
   Total[Table[v[[i]], {i, n/2 + 1, n}]]] == constant5

v[[n - 1]] == penultimateValue
v[[n - 1]] > 0

Table[v[[i]] + v[[n - i + 1]] == constant2, {i, 1, n/2}]

Total[Table[v[[i]], {i, 1, n}]] == constant1

Total[Table[v[[i]], {i, 1, n}]] ==
 Total[Table[v[[i]], {i, n/2 - n/4 + 1, n/2 + n/4}]]*2
Total[Table[v[[i]], {i, n/2 - n/4 + 1, n/2 + n/4}]] ==
 Total[Table[v[[i]], {i, n/2 - n/8 + 1, n/2 + n/8}]]*2

(*for n=480 etc: (can add more of these)*)
If[n >= 480,
 Total[Table[v[[i]], {i, n/2 - n/8 + 1, n/2 + n/8}]] ==
  Total[Table[v[[i]], {i, n/2 - n/16 + 1, n/2 + n/16}]]*2
 ]

Table[v[[i]] - v[[i + 1]] == v[[n - i]] - v[[n - i + 1]], {i, 1,
  n/2 - 1}]

v[[n/2]] - v[[n/2 + 1]] == v[[n/2 - 2]] - v[[n/2 - 1]]
v[[n/2]] - v[[n/2 + 1]] == v[[n/2 + 2]] - v[[n/2 + 3]]
v[[1]] - v[[n]] == constant3
v[[n]] - v[[1]] == -constant3

Total[Abs[Table[v[[i]] - v[[i + 1]], {i, 1, n - 1}]]] == constant4

Total[Table[v[[i]] - v[[i + 1]], {i, 1, n - 1}]] == constant3

Abs[Min[Table[v[[i]] - v[[i + 1]], {i, 1, n - 1}]]] == constant3

Min[Table[v[[i]] - v[[i + 1]], {i, 1, n - 1}]] == -constant3

Max[Table[v[[i]] - v[[i + 1]], {i, 1, n - 1}]] == constant6