A242506 Number of compositions of n, where the difference between the number of odd parts and the number of even parts is 8.

1, 0, 8, 10, 36, 100, 186, 550, 1122, 2564, 5940, 12246, 27560, 58240, 122642, 262458, 542243, 1134944, 2352136, 4826980, 9949352, 20300312, 41377116, 84172508, 170322099, 344527304, 694617960, 1397219682, 2807142612, 5625453196, 11258808682, 22498804286

Offset

8,3

Comments

With offset 16 number of compositions of n, where the difference between the number of odd parts and the number of even parts is -8.

Links

Alois P. Heinz, Table of n, a(n) for n = 8..1000

Formula

Recurrence (for n>=12): (n-8)*(n+16)*(2*n+1)*(2*n+3)*(n^4 + 6*n^3 + 11*n^2 + 6*n - 4096)*a(n) = -256*(n-9)*(n+1)*(n+15)*(2*n+1)*(2*n+5)*a(n-1) + 2*(2*n+3)*(2*n^7 + 27*n^6 + 242*n^5 + 549*n^4 - 9408*n^3 - 49916*n^2 - 462064*n - 606208)*a(n-2) + 2*(n+1)*(2*n+1)*(2*n+5)*(2*n^5 + 21*n^4 + 79*n^3 + 254*n^2 - 7608*n - 5760)*a(n-3) - (n-4)*(n+4)*(2*n+3)*(2*n+5)*(n^4 + 10*n^3 + 35*n^2 + 50*n - 4072)*a(n-4). - Vaclav Kotesovec, May 20 2014

Crossrefs

Column k=8 of A242498.

Sequence in context: A302312 A245199 A303042 * A302879 A303527 A367893

Adjacent sequences: A242503 A242504 A242505 * A242507 A242508 A242509

Keyword

nonn

Author

Alois P. Heinz, May 16 2014

Status

approved