A381290 Number of subsets of 6 integers between 1 and n such that their sum is 1 modulo n.

1, 4, 9, 22, 42, 78, 132, 217, 333, 504, 728, 1035, 1428, 1944, 2583, 3399, 4389, 5616, 7084, 8866, 10962, 13468, 16380, 19806, 23751, 28336, 33561, 39576, 46376, 54126, 62832, 72675, 83655, 95988, 109668, 124929, 141778, 160468, 180999

Offset

7,2

Comments

For s an integer such that GCD(s,6)=1, 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 + 2*x + 3*x^3 + 2*x^4 + 2*x^5 + x^6 + x^7)/((1 - x)^2*(1 - x^2)^2*(1 - x^3)*(1 - x^6)).

Example

For n=7, a(7)=1 since the set {0,1,2,3,4,5} is the unique order 6 subset of Z/7Z with sum equal to 1 mod 7.

Crossrefs

Cf. A381289, A011796.

Sequence in context: A290647 A105314 A200155 * A002835 A253289 A032288

Adjacent sequences: A381285 A381286 A381289 * A381291 A381292 A381293

Keyword

nonn,easy

Author

Xavier Roulleau and David Broadhurst, Feb 19 2025

Status

approved