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

Author

Xavier Roulleau and David Broadhurst, Feb 19 2025

Keywords

• nonn
• easy

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.

Examples

			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.
		

Links

• 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).

Crossrefs

Cf. A381289, A011796.

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)).