# Fredholm Rueppel sequences

Apr 21st, 2013
179
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1. (*Mathematica 8*)
2. (*program start*)
3. Clear[t];
4. modulus = 1;
5. nn = 100;
6. t[n_, 1] = 1;
7. t[1, k_] = 1;
8. t[n_, k_] :=
9. t[n, k] =
10. If[n < k,
11. If[And[n > 1, k > 1], Sum[-t[k - i, n], {i, 1, n - 1}], 0],
12. If[And[n > 1, k > 1], Sum[-t[n - i, k], {i, 1, k - 1}], 0]];
13. Table[Total[
14. Table[t[n, k]*
15. If[And[Mod[n, modulus] == 0, Mod[k, modulus] == 0], 1 - modulus,
16. 1], {k, 1, n}]], {n, 1, nn}]
17. (*program end*)
18. (*program start*)
19. Clear[t];
20. modulus = 2;
21. nn = 100;
22. t[n_, 1] = 1;
23. t[1, k_] = 1;
24. t[n_, k_] :=
25. t[n, k] =
26. If[n < k,
27. If[And[n > 1, k > 1], Sum[-t[k - i, n], {i, 1, n - 1}], 0],
28. If[And[n > 1, k > 1], Sum[-t[n - i, k], {i, 1, k - 1}], 0]];
29. Table[Total[
30. Table[t[n, k]/
31. If[And[Mod[n, modulus] == 0, Mod[k, modulus] == 0], 1 - modulus,
32. 1], {k, 1, n}]], {n, 1, nn}]
33. (*program end*)
34. (*program start*)
35. Clear[t];
36. modulus = 3;
37. nn = 100;
38. t[n_, 1] = 1;
39. t[1, k_] = 1;
40. t[n_, k_] :=
41. t[n, k] =
42. If[n < k,
43. If[And[n > 1, k > 1], Sum[-t[k - i, n], {i, 1, n - 1}], 0],
44. If[And[n > 1, k > 1], Sum[-t[n - i, k], {i, 1, k - 1}], 0]];
45. Table[Total[
46. Table[t[n, k]/
47. If[And[Mod[n, modulus] == 0, Mod[k, modulus] == 0], 1 - modulus,
48. 1], {k, 1, n}]], {n, 1, nn}]
49. (*program end*)
50. (*program start*)
51. Clear[t];
52. modulus = 4;
53. nn = 100;
54. t[n_, 1] = 1;
55. t[1, k_] = 1;
56. t[n_, k_] :=
57. t[n, k] =
58. If[n < k,
59. If[And[n > 1, k > 1], Sum[-t[k - i, n], {i, 1, n - 1}], 0],
60. If[And[n > 1, k > 1], Sum[-t[n - i, k], {i, 1, k - 1}], 0]];
61. Table[Total[
62. Table[t[n, k]*
63. If[And[Mod[n, modulus] == 0, Mod[k, modulus] == 0], 1 - modulus,
64. 1], {k, 1, n}]], {n, 1, nn}]
65. (*program end*)
66. (*program start*)
67. Clear[t];
68. modulus = 5;
69. nn = 100;
70. t[n_, 1] = 1;
71. t[1, k_] = 1;
72. t[n_, k_] :=
73. t[n, k] =
74. If[n < k,
75. If[And[n > 1, k > 1], Sum[-t[k - i, n], {i, 1, n - 1}], 0],
76. If[And[n > 1, k > 1], Sum[-t[n - i, k], {i, 1, k - 1}], 0]];
77. Table[Total[
78. Table[t[n, k]/
79. If[And[Mod[n, modulus] == 0, Mod[k, modulus] == 0], 1 - modulus,
80. 1], {k, 1, n}]], {n, 1, nn}]
81. (*program end*)
82. (*program start*)
83. Clear[t];
84. modulus = 6;
85. nn = 100;
86. t[n_, 1] = 1;
87. t[1, k_] = 1;
88. t[n_, k_] :=
89. t[n, k] =
90. If[n < k,
91. If[And[n > 1, k > 1], Sum[-t[k - i, n], {i, 1, n - 1}], 0],
92. If[And[n > 1, k > 1], Sum[-t[n - i, k], {i, 1, k - 1}], 0]];
93. Table[Total[
94. Table[t[n, k]*
95. If[And[Mod[n, modulus] == 0, Mod[k, modulus] == 0], 1 - modulus,
96. 1], {k, 1, n}]], {n, 1, nn}]
97. (*program end*)
98. (*program start*)
99. Clear[t];
100. modulus = 7;
101. nn = 100;
102. t[n_, 1] = 1;
103. t[1, k_] = 1;
104. t[n_, k_] :=
105. t[n, k] =
106. If[n < k,
107. If[And[n > 1, k > 1], Sum[-t[k - i, n], {i, 1, n - 1}], 0],
108. If[And[n > 1, k > 1], Sum[-t[n - i, k], {i, 1, k - 1}], 0]];
109. Table[Total[
110. Table[t[n, k]/
111. If[And[Mod[n, modulus] == 0, Mod[k, modulus] == 0], 1 - modulus,
112. 1], {k, 1, n}]], {n, 1, nn}]
113. (*program end*)
114. (*program start*)
115. Clear[t];
116. modulus = 8;
117. nn = 100;
118. t[n_, 1] = 1;
119. t[1, k_] = 1;
120. t[n_, k_] :=
121. t[n, k] =
122. If[n < k,
123. If[And[n > 1, k > 1], Sum[-t[k - i, n], {i, 1, n - 1}], 0],
124. If[And[n > 1, k > 1], Sum[-t[n - i, k], {i, 1, k - 1}], 0]];
125. Table[Total[
126. Table[t[n, k]*
127. If[And[Mod[n, modulus] == 0, Mod[k, modulus] == 0], 1 - modulus,
128. 1], {k, 1, n}]], {n, 1, nn}]
129. (*program end*)
130. (*program start*)
131. Clear[t];
132. modulus = 9;
133. nn = 100;
134. t[n_, 1] = 1;
135. t[1, k_] = 1;
136. t[n_, k_] :=
137. t[n, k] =
138. If[n < k,
139. If[And[n > 1, k > 1], Sum[-t[k - i, n], {i, 1, n - 1}], 0],
140. If[And[n > 1, k > 1], Sum[-t[n - i, k], {i, 1, k - 1}], 0]];
141. Table[Total[
142. Table[t[n, k]*
143. If[And[Mod[n, modulus] == 0, Mod[k, modulus] == 0], 1 - modulus,
144. 1], {k, 1, n}]], {n, 1, nn}]
145. (*program end*)
146. (*program start*)
147. Clear[t];
148. modulus = 10;
149. nn = 100;
150. t[n_, 1] = 1;
151. t[1, k_] = 1;
152. t[n_, k_] :=
153. t[n, k] =
154. If[n < k,
155. If[And[n > 1, k > 1], Sum[-t[k - i, n], {i, 1, n - 1}], 0],
156. If[And[n > 1, k > 1], Sum[-t[n - i, k], {i, 1, k - 1}], 0]];
157. Table[Total[
158. Table[t[n, k]*
159. If[And[Mod[n, modulus] == 0, Mod[k, modulus] == 0], 1 - modulus,
160. 1], {k, 1, n}]], {n, 1, nn}]
161. (*program end*)
162. (*program start*)
163. Clear[t];
164. modulus = 11;
165. nn = 100;
166. t[n_, 1] = 1;
167. t[1, k_] = 1;
168. t[n_, k_] :=
169. t[n, k] =
170. If[n < k,
171. If[And[n > 1, k > 1], Sum[-t[k - i, n], {i, 1, n - 1}], 0],
172. If[And[n > 1, k > 1], Sum[-t[n - i, k], {i, 1, k - 1}], 0]];
173. Table[Total[
174. Table[t[n, k]/
175. If[And[Mod[n, modulus] == 0, Mod[k, modulus] == 0], 1 - modulus,
176. 1], {k, 1, n}]], {n, 1, nn}]
177. (*program end*)
178. (*program start*)
179. Clear[t];
180. modulus = 12;
181. nn = 100;
182. t[n_, 1] = 1;
183. t[1, k_] = 1;
184. t[n_, k_] :=
185. t[n, k] =
186. If[n < k,
187. If[And[n > 1, k > 1], Sum[-t[k - i, n], {i, 1, n - 1}], 0],
188. If[And[n > 1, k > 1], Sum[-t[n - i, k], {i, 1, k - 1}], 0]];
189. Table[Total[
190. Table[t[n, k]*
191. If[And[Mod[n, modulus] == 0, Mod[k, modulus] == 0], 1 - modulus,
192. 1], {k, 1, n}]], {n, 1, nn}]
193. (*program end*)
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