A318625 Number of 4-member subsets of [4*n] whose elements sum to a multiple of n.

0, 1, 38, 165, 460, 969, 1782, 2925, 4508, 6545, 9158, 12341, 16236, 20825, 26262, 32509, 39740, 47905, 57190, 67525, 79116, 91881, 106038, 121485, 138460, 156849, 176902, 198485, 221868, 246905, 273878, 302621, 333436, 366145, 401062, 437989, 477260, 518665

Offset: 0

Author

Alois P. Heinz, Aug 30 2018

Keywords

• nonn
• easy

Examples

			a(2) = 38: {1,2,3,4}, {1,2,3,6}, {1,2,3,8}, {1,2,4,5}, {1,2,4,7}, {1,2,5,6}, {1,2,5,8}, {1,2,6,7}, {1,2,7,8}, {1,3,4,6}, {1,3,4,8}, {1,3,5,7}, {1,3,6,8}, {1,4,5,6}, {1,4,5,8}, {1,4,6,7}, {1,4,7,8}, {1,5,6,8}, {1,6,7,8}, {2,3,4,5}, {2,3,4,7}, {2,3,5,6}, {2,3,5,8}, {2,3,6,7}, {2,3,7,8}, {2,4,5,7}, {2,4,6,8}, {2,5,6,7}, {2,5,7,8}, {3,4,5,6}, {3,4,5,8}, {3,4,6,7}, {3,4,7,8}, {3,5,6,8}, {3,6,7,8}, {4,5,6,7}, {4,5,7,8}, {5,6,7,8}.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (2,0,-2,2,-2,0,2,-1).

Crossrefs

Row n=4 of A318557.

Formula

G.f.: x*(4*x^7+27*x^6+100*x^5+123*x^4+132*x^3+89*x^2+36*x+1) / ((x^2+1) *(x+1)^2 *(x-1)^4).