A318593 Number of n-member subsets of [5*n] whose elements sum to a multiple of five.

1, 1, 9, 91, 969, 10630, 118755, 1344904, 15380937, 177232627, 2054455670, 23930713170, 279871768995, 3284214703056, 38650751381832, 456002537343580, 5391644226101705, 63871405575418665, 757929628541719755, 9007607943130625829, 107196674080761940470

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..922

Formula

a(n) = floor(A163456(n)) + [n mod 5 = 0]*A163455(n/5), with A163456(n) = binomial(5*n,n)/5 and A163455(n) = binomial(5*n-1,n) where [] is an Iverson bracket. - Georg Fischer, Mar 23 2019

Example

a(2) = 9: {1,4}, {1,9}, {2,3}, {2,8}, {3,7}, {4,6}, {5,10}, {6,9}, {7,8}.

Maple

b:= proc(n, s, m, t) option remember; `if`(n=0, `if`(s=0 and t=0, 1, 0),
      b(n-1, s, m, t)+`if`(t=0, 0, b(n-1, irem(s+n, m), m, t-1)))
    end:
a:= n-> b(5*n, 0, 5, n):
seq(a(n), n=0..27);

Crossrefs

Column k=5 of A318557.

Cf. A163455, A163456.

Sequence in context: A242299 A109108 A163456 * A362728 A335508 A176735

Adjacent sequences: A318590 A318591 A318592 * A318594 A318595 A318596

Keyword

nonn

Author

Alois P. Heinz, Aug 29 2018

Status

approved