%I #7 May 20 2014 02:43:20

%S 1,0,6,8,21,64,101,288,576,1180,2727,5280,11363,23496,46981,98176,

%T 196482,397644,806351,1606488,3234335,6456048,12849330,25637632,

%U 50835950,100883304,199903578,395067760,781029504,1540973568,3037666097,5984978112,11775884581

%N Number of compositions of n, where the difference between the number of odd parts and the number of even parts is 6.

%C With offset 12 number of compositions of n, where the difference between the number of odd parts and the number of even parts is -6.

%H Alois P. Heinz, <a href="/A242504/b242504.txt">Table of n, a(n) for n = 6..1000</a>

%F Recurrence (for n>=10): (n-6)*(n+12)*(2*n-1)*(2*n+1)*(n^4 + 2*n^3 - n^2 - 2*n - 1296)*a(n) = -144*(n-7)*n*(n+11)*(2*n-1)*(2*n+3)*a(n-1) + 2*(2*n+1)*(2*n^7 + 13*n^6 + 80*n^5 - 179*n^4 - 3424*n^3 - 6476*n^2 - 69072*n - 31104)*a(n-2) + 2*n*(2*n-1)*(2*n+3)*(2*n^5 + 11*n^4 + 15*n^3 + 67*n^2 - 2465*n + 642)*a(n-3) - (n-4)*(n+2)*(2*n+1)*(2*n+3)*(n^4 + 6*n^3 + 11*n^2 + 6*n - 1296)*a(n-4). - _Vaclav Kotesovec_, May 20 2014

%Y Column k=6 of A242498.

%K nonn

%O 6,3

%A _Alois P. Heinz_, May 16 2014