A318628 Number of 7-member subsets of [7*n] whose elements sum to a multiple of n.

0, 1, 1716, 38760, 296010, 1344904, 4496388, 12271518, 28989675, 61474519, 119877472, 218618940, 377447148, 622614630, 988172374, 1517381580, 2264243157, 3295144749, 4690625500, 6547258432, 8979650478, 12122560170, 16133132940, 21193254160, 27512019711

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 (6,-15,20,-15,6,-1,1,-6,15,-20,15,-6,1).

Formula

G.f.: -x*(7*x^12 +1674*x^11 +28569*x^10 +89050*x^9 +116029*x^8 +117612*x^7 +117655*x^6 +117648*x^5 +115939*x^4 +89170*x^3 +28479*x^2 +1710*x+1) / ((x^6+x^5+x^4+x^3+x^2+x+1) *(x-1)^7).

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) + a(n-7) - 6*a(n-8) + 15*a(n-9) - 20*a(n-10) + 15*a(n-11) - 6*a(n-12) + a(n-13). - Wesley Ivan Hurt, Mar 25 2023

Crossrefs

Row n=7 of A318557.

Sequence in context: A185795 A260474 A222343 * A194719 A140910 A208620

Adjacent sequences: A318625 A318626 A318627 * A318629 A318630 A318631

Keyword

nonn,easy

Author

Alois P. Heinz, Aug 30 2018

Status

approved