A381289 Number of subsets of 6 integers between 1 and n such that their sum is 0 modulo n.

1, 3, 10, 20, 42, 76, 132, 212, 335, 497, 728, 1028, 1428, 1932, 2586, 3384, 4389, 5601, 7084, 8844, 10966, 13442, 16380, 19780, 23751, 28301, 33566, 39536, 46376, 54086, 62832, 72624, 83661, 95931, 109668, 124872, 141778, 160398, 181006

Offset

7,2

Comments

For an integer s multiple of 6, this is also the number of subsets of 6 integers between 1 and n such that their sum is s modulo n.

Links

Table of n, a(n) for n=7..45.

David Broadhurst and Xavier Roulleau, Number of partitions of modular integers, arXiv:2502.19523 [math.NT], 2025.

Index entries for linear recurrences with constant coefficients, signature (2,1,-3,-1,1,4,-3,-3,4,1,-1,-3,1,2,-1).

Formula

G.f.: x^7*(1 + x + 3*x^2 + 2*x^4 + 4*x^5 + x^6 - x^7 + x^8)/((1 - x)^2*(1 - x^2)^2*(1 - x^3)*(1 - x^6)). - David Broadhurst, Feb 19 2025

Example

For n=8, there are a(8)=3 order 6 subsets of Z/8Z with sum equal to 0 mod 8.

Crossrefs

Cf. A011796.

Sequence in context: A295953 A005997 A213850 * A336529 A081205 A273379

Adjacent sequences: A381284 A381285 A381286 * A381290 A381291 A381292

Keyword

nonn,easy

Author

Xavier Roulleau and David Broadhurst, Feb 19 2025

Status

approved