A318626 Number of 5-member subsets of [5*n] whose elements sum to a multiple of n.

0, 1, 126, 1001, 3876, 10630, 23751, 46376, 82251, 135751, 211880, 316251, 455126, 635376, 864501, 1150630, 1502501, 1929501, 2441626, 3049501, 3764380, 4598126, 5563251, 6672876, 7940751, 9381255, 11009376, 12840751, 14891626, 17178876, 19720005, 22533126

Offset: 0

Author

Alois P. Heinz, Aug 30 2018

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1,1,-4,6,-4,1).

Crossrefs

Row n=5 of A318557.

Programs

Mathematica

LinearRecurrence[{4,-6,4,-1,1,-4,6,-4,1},{0,1,126,1001,3876,10630,23751,46376,82251,135751},40] (* Harvey P. Dale, Jul 13 2019 *)

Formula

G.f.: -x*(5*x^8+106*x^7+527*x^6+608*x^5+629*x^4+624*x^3+503*x^2+122*x+1) / ((x^4+x^3+x^2+x+1) *(x-1)^5).

a(n) = (-250*n +216/5 + 625*n^4 -1250*n^3 +875*n^2)/24 +4* b(n)/5 for n>=1, where b(n) = b(n-5) = 4, -1, -1, -1, -1, 4, -1, -1, -1,.. 5-periodic for n>=0. - R. J. Mathar, Apr 17 2024