A381351 Number of subsets of 9 integers between 1 and n such that their sum is 3 modulo n.

1, 5, 19, 55, 143, 335, 715, 1430, 2703, 4862, 8398, 14000, 22610, 35530, 54484, 81719, 120175, 173592, 246675, 345345, 476913, 650325, 876525, 1168710, 1542684, 2017356, 2615103, 3362260, 4289780, 5433736, 6835972, 8544965, 10616489, 13114465

Offset: 10

Author

Xavier Roulleau, Feb 21 2025

Keywords

• nonn
• easy

Comments

For s an integer such that GCD(s,9)=3, this is also the number of subsets of 9 integers between 1 and n such that their sum is s modulo n.

Examples

			For n=10, there are a(10)=1 order 9 subsets of Z/10Z with sum equal to 3 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 (6,-15,22,-27,36,-42,36,-27,23,-21,21,-23,27,-36,42,-36,27,-22,15,-6,1).

Crossrefs

Cf. A011796, A031164, A032194, A381289, A381290, A381291.

Formula

G.f.: x^10*(1 - x + 4*x^2 - 6*x^3 + 15*x^4 - 17*x^5 + 15*x^6 - 6*x^7 + 4*x^8 - x^9 + x^10)/((1 - x)^6*(1 - x^3)^2*(1 - x^9)).