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

0,3

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).

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).

Example

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}.

Crossrefs

Row n=4 of A318557.

Sequence in context: A251253 A224739 A135176 * A281208 A100167 A100168

Adjacent sequences: A318622 A318623 A318624 * A318626 A318627 A318628

Keyword

nonn,easy

Author

Alois P. Heinz, Aug 30 2018

Status

approved