A242502 Number of compositions of n, where the difference between the number of odd parts and the number of even parts is 4.

1, 0, 4, 6, 10, 36, 48, 126, 259, 456, 1064, 1956, 3939, 8112, 15300, 31174, 60951, 118580, 236456, 458172, 900185, 1765556, 3431792, 6728410, 13107393, 25538448, 49856392, 96966572, 188914574, 367741688, 715053048, 1391512424, 2705016795, 5258241032

Offset

4,3

Comments

With offset 8 number of compositions of n, where the difference between the number of odd parts and the number of even parts is -4.

Links

Alois P. Heinz, Table of n, a(n) for n = 4..1000

Formula

Recurrence (for n>=8): (n-4)*(n+8)*(2*n-3)*(2*n-1)*(n^4 - 2*n^3 - n^2 + 2*n - 256)*a(n) = -64*(n-5)*(n-1)*(n+7)*(2*n-3)*(2*n+1)*a(n-1) + 2*(2*n-1)*(2*n^7 - n^6 + 14*n^5 - 199*n^4 - 288*n^3 + 600*n^2 - 5360*n + 2928)*a(n-2) + 2*(n-1)*(2*n-3)*(2*n+1)*(2*n^5 + n^4 - 9*n^3 + 28*n^2 - 508*n + 608)*a(n-3) - (n-4)*n*(2*n-1)*(2*n+1)*(n^4 + 2*n^3 - n^2 - 2*n - 256)*a(n-4). - Vaclav Kotesovec, May 20 2014

Crossrefs

Column k=4 of A242498.

Sequence in context: A032392 A253048 A271956 * A136838 A234276 A274991

Adjacent sequences: A242499 A242500 A242501 * A242503 A242504 A242505

Keyword

nonn

Author

Alois P. Heinz, May 16 2014

Status

approved