A242501 Number of compositions of n, where the difference between the number of odd parts and the number of even parts is 3.

1, 0, 3, 5, 6, 25, 31, 75, 162, 259, 609, 1106, 2122, 4410, 8076, 16197, 31527, 59961, 118844, 227700, 441507, 860860, 1654731, 3218501, 6226818, 12027405, 23337471, 45082050, 87258876, 168935018, 326536646, 632132760, 1222716653, 2364969824, 4576680195

Offset

3,3

Comments

With offset 6 number of compositions of n, where the difference between the number of odd parts and the number of even parts is -3.

Links

Alois P. Heinz, Table of n, a(n) for n = 3..1000

Formula

Recurrence (for n>=7): (n-3)*(n-2)*(n-1)*(n+6)*(16*n^4 - 64*n^3 + 56*n^2 + 16*n - 1311)*a(n) = -288*(n-4)*(n-2)*n*(n+5)*(2*n-3)*a(n-1) + 2*(n-1)*(16*n^7 - 64*n^6 + 136*n^5 - 1048*n^4 + 1621*n^3 + 1202*n^2 - 9162*n + 7866)*a(n-2) + 2*(n-2)*n*(2*n-3)*(16*n^5 - 32*n^4 - 48*n^3 + 212*n^2 - 1429*n + 2145)*a(n-3) - (n-4)*(n-1)^2*n*(16*n^4 - 40*n^2 - 1287)*a(n-4). - Vaclav Kotesovec, May 20 2014

Crossrefs

Column k=3 of A242498.

Sequence in context: A103022 A086189 A137082 * A099414 A004785 A099744

Adjacent sequences: A242498 A242499 A242500 * A242502 A242503 A242504

Keyword

nonn

Author

Alois P. Heinz, May 16 2014

Status

approved