A242500 Number of compositions of n, where the difference between the number of odd parts and the number of even parts is 2.

1, 0, 2, 4, 3, 16, 19, 40, 95, 136, 321, 588, 1057, 2240, 3998, 7848, 15339, 28464, 56143, 106788, 204083, 396704, 755052, 1457456, 2806531, 5377112, 10382243, 19947252, 38382957, 73996576, 142311198, 274283168, 528438319, 1017784016, 1962451118, 3781912684

Offset

2,3

Comments

With offset 4 number of compositions of n, where the difference between the number of odd parts and the number of even parts is -2.

Links

Alois P. Heinz, Table of n, a(n) for n = 2..1000

Formula

Recurrence (for n>=6): (n+4)*(2*n-5)*(2*n-3)*(n^4 - 6*n^3 + 11*n^2 - 6*n - 16)*a(n) = -16*(n-3)*(n+3)*(2*n-5)*(2*n-1)*a(n-1) + 2*(n-2)*(2*n-3)*(2*n^5 - 7*n^4 + 8*n^3 - 51*n^2 + 28*n + 32)*a(n-2) + 2*(n-3)*(2*n-5)*(2*n-1)*(2*n^4 - 3*n^3 - 2*n^2 + 11*n - 24)*a(n-3) - (n-4)*(2*n-3)*(2*n-1)*(n^4 - 2*n^3 - n^2 + 2*n - 16)*a(n-4). - Vaclav Kotesovec, May 20 2014

Crossrefs

Column k=2 of A242498.

Sequence in context: A225546 A329050 A053124 * A132049 A229213 A356063

Adjacent sequences: A242497 A242498 A242499 * A242501 A242502 A242503

Keyword

nonn

Author

Alois P. Heinz, May 16 2014

Status

approved