A242505 Number of compositions of n, where the difference between the number of odd parts and the number of even parts is 7.

1, 0, 7, 9, 28, 81, 139, 405, 815, 1771, 4092, 8173, 18019, 37609, 77246, 163345, 331968, 683631, 1400777, 2832362, 5770056, 11640546, 23446366, 47227530, 94582628, 189487950, 378658714, 754877809, 1504215522, 2990469337, 5939101301, 11782590061, 23340439078

Offset

7,3

Comments

With offset 14 number of compositions of n, where the difference between the number of odd parts and the number of even parts is -7.

Links

Alois P. Heinz, Table of n, a(n) for n = 7..1000

Formula

Recurrence (for n>=11): (n-7)*n*(n+1)*(n+14)*(16*n^4 + 64*n^3 + 56*n^2 - 16*n - 38431)*a(n) = -1568*(n-8)*n*(n+2)*(n+13)*(2*n+1)*a(n-1) + 2*(n+1)*(16*n^7 + 160*n^6 + 1192*n^5 + 472*n^4 - 49083*n^3 - 168912*n^2 - 1534048*n - 1379196)*a(n-2) + 2*n*(n+2)*(2*n+1)*(16*n^5 + 128*n^4 + 336*n^3 + 1076*n^2 - 36101*n - 8729)*a(n-3) - (n-4)*(n+1)*(n+2)*(n+3)*(16*n^4 + 128*n^3 + 344*n^2 + 352*n - 38311)*a(n-4). - Vaclav Kotesovec, May 20 2014

Crossrefs

Column k=7 of A242498.

Sequence in context: A113124 A324986 A030404 * A263826 A066930 A247192

Adjacent sequences: A242502 A242503 A242504 * A242506 A242507 A242508

Keyword

nonn

Author

Alois P. Heinz, May 16 2014

Status

approved