Partitions of {1,...,3n} into triples where x + y = 3z

n = 8:

[18, 3, 7]
[24, 6, 10]
[21, 15, 12]
[17, 16, 11]
[4, 9, 23]
[1, 5, 14]
[2, 8, 22]
[13, 20, 19]

n = 5:

[12, 9, 7]
[15, 3, 6]
[8, 14, 10]
[13, 2, 5]
[1, 4, 11]

n = 16:

[36, 3, 13]
[2, 5, 1]
[4, 6, 14]
[8, 17, 7]
[9, 16, 11]
[10, 18, 12]
[15, 26, 19]
[33, 27, 20]
[39, 28, 45]
[48, 42, 30]
[44, 43, 29]
[46, 31, 47]
[21, 41, 22]
[23, 37, 32]
[24, 38, 34]
[25, 40, 35]

n = 13:

[30, 3, 11]
[1, 2, 5]
[4, 6, 14]
[34, 20, 18]
[33, 12, 15]
[24, 37, 35]
[26, 25, 17]
[28, 19, 29]
[36, 27, 21]
[9, 16, 39]
[22, 8, 10]
[7, 13, 32]
[23, 38, 31]

n = 24:

[48, 3, 17]
[1, 2, 5]
[4, 6, 14]
[7, 13, 8]
[9, 16, 11]
[10, 18, 12]
[15, 26, 19]
[54, 21, 25]
[51, 30, 27]
[57, 36, 31]
[66, 39, 35]
[60, 24, 28]
[63, 45, 72]
[69, 42, 37]
[20, 23, 49]
[22, 29, 65]
[47, 71, 70]
[50, 34, 52]
[44, 68, 64]
[46, 33, 53]
[43, 67, 62]
[41, 32, 55]
[38, 58, 56]
[40, 61, 59]

n = 21:

[42, 3, 15]
[48, 6, 18]
[45, 12, 19]
[54, 9, 21]
[60, 24, 28]
[51, 27, 26]
[57, 30, 29]
[63, 33, 32]
[39, 36, 25]
[41, 1, 14]
[40, 8, 16]
[44, 7, 17]
[61, 5, 22]
[4, 10, 2]
[11, 20, 49]
[13, 23, 56]
[37, 58, 53]
[46, 31, 47]
[34, 59, 43]
[35, 55, 50]
[38, 62, 52]

n = 32:

[66, 3, 23]
[1, 2, 5]
[4, 6, 14]
[7, 13, 8]
[9, 17, 10]
[11, 21, 12]
[15, 29, 16]
[18, 35, 19]
[20, 38, 22]
[64, 26, 30]
[24, 47, 25]
[73, 44, 39]
[27, 53, 28]
[72, 48, 40]
[63, 33, 32]
[65, 37, 34]
[31, 57, 36]
[90, 75, 55]
[78, 45, 41]
[81, 69, 50]
[84, 59, 93]
[87, 61, 96]
[60, 95, 85]
[88, 86, 58]
[68, 46, 70]
[83, 43, 42]
[54, 91, 71]
[49, 80, 67]
[82, 74, 52]
[51, 77, 76]
[56, 89, 79]
[62, 94, 92]

n = 29:

[60, 3, 21]
[66, 6, 24]
[63, 12, 25]
[72, 9, 27]
[78, 15, 31]
[75, 30, 35]
[57, 39, 32]
[84, 18, 34]
[69, 42, 37]
[81, 33, 38]
[54, 47, 87]
[51, 36, 29]
[48, 86, 58]
[82, 2, 28]
[61, 5, 22]
[62, 7, 23]
[1, 4, 11]
[13, 10, 17]
[8, 16, 40]
[20, 46, 14]
[19, 26, 59]
[64, 43, 65]
[68, 67, 45]
[55, 44, 77]
[56, 85, 83]
[52, 80, 76]
[53, 41, 70]
[49, 74, 73]
[50, 79, 71]

n = 40:

[84, 3, 29]
[1, 2, 5]
[4, 6, 14]
[7, 13, 8]
[9, 17, 10]
[11, 21, 12]
[15, 27, 18]
[16, 28, 20]
[19, 35, 22]
[23, 45, 24]
[25, 49, 26]
[96, 30, 42]
[87, 33, 40]
[81, 36, 39]
[31, 61, 32]
[34, 65, 37]
[90, 48, 46]
[78, 51, 43]
[120, 54, 58]
[38, 73, 41]
[102, 57, 53]
[99, 66, 55]
[93, 67, 108]
[105, 72, 111]
[114, 77, 117]
[75, 119, 106]
[83, 56, 85]
[44, 82, 50]
[47, 89, 52]
[80, 59, 97]
[79, 60, 101]
[86, 62, 100]
[88, 64, 104]
[103, 70, 107]
[92, 68, 112]
[110, 76, 118]
[71, 115, 98]
[63, 95, 94]
[69, 116, 91]
[74, 113, 109]

n = 37:

[78, 3, 27]
[75, 9, 28]
[84, 6, 30]
[90, 12, 34]
[81, 15, 32]
[96, 18, 38]
[93, 24, 39]
[102, 21, 41]
[72, 33, 35]
[87, 42, 43]
[105, 36, 47]
[108, 45, 51]
[99, 48, 49]
[111, 54, 55]
[69, 63, 44]
[66, 110, 88]
[60, 109, 71]
[79, 8, 29]
[77, 1, 26]
[73, 2, 25]
[4, 7, 5]
[10, 19, 11]
[14, 22, 20]
[13, 23, 16]
[17, 31, 76]
[37, 61, 50]
[83, 56, 85]
[40, 74, 46]
[80, 57, 91]
[82, 59, 95]
[86, 62, 100]
[64, 103, 89]
[92, 67, 53]
[52, 98, 58]
[65, 101, 94]
[68, 107, 97]
[70, 106, 104]

n = 48:

[96, 3, 33]
[102, 6, 36]
[99, 12, 37]
[108, 9, 39]
[114, 15, 43]
[105, 18, 41]
[120, 21, 47]
[111, 24, 45]
[126, 27, 51]
[123, 42, 55]
[117, 30, 49]
[132, 48, 60]
[138, 54, 64]
[129, 57, 62]
[144, 63, 69]
[135, 66, 67]
[93, 75, 56]
[141, 72, 71]
[90, 84, 58]
[87, 143, 118]
[81, 78, 53]
[101, 1, 34]
[95, 10, 35]
[97, 17, 38]
[103, 29, 44]
[4, 7, 5]
[2, 8, 22]
[20, 13, 11]
[14, 26, 16]
[25, 19, 32]
[23, 28, 61]
[31, 40, 89]
[46, 88, 50]
[52, 59, 125]
[94, 68, 110]
[100, 73, 119]
[92, 142, 134]
[139, 98, 79]
[130, 116, 82]
[106, 104, 70]
[124, 107, 77]
[76, 115, 113]
[80, 131, 109]
[140, 133, 91]
[65, 121, 74]
[85, 128, 127]
[83, 137, 112]
[86, 136, 122]