A381291 Number of subsets of 8 integers between 1 and n such that their sum is 0 modulo n.

1, 5, 15, 43, 99, 217, 429, 809, 1430, 2438, 3978, 6310, 9690, 14550, 21318, 30666, 43263, 60115, 82225, 111041, 148005, 195143, 254475, 328755, 420732, 534076, 672452, 840652, 1043460, 1287036, 1577532, 1922740, 2330445, 2810385, 3372291, 4028183, 4790071

Offset: 9

Author

Xavier Roulleau and David Broadhurst, Feb 19 2025

Keywords

• nonn

Comments

For an integer s multiple of 8, this is also the number of subsets of 8 integers between 1 and n such that their sum is s modulo n.

Examples

			For n=10, there are a(10)=5 order 8 subsets of Z/10Z with sum equal to 0 mod 10.
		

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 (4,-4,-4,11,-8,0,8,-10,0,8,0,-10,8,0,-8,11,-4,-4,4,-1).

Crossrefs

Cf. A381290, A381289, A011796.

Formula

G.f.: x^9*(1 + x - x^2 + 7*x^3 - 4*x^4 + 6*x^5 + 4*x^6 - 4*x^7 + 3*x^8 + 5*x^9 - 3*x^10 + x^11)/((1 - x)^4*(1 - x^2)^2*(1 - x^4)*(1 - x^8)).