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

Author

Alois P. Heinz, May 16 2014

Keywords

• nonn

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

Crossrefs

Column k=3 of A242498.

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