%I #7 May 20 2014 02:40:37
%S 1,0,2,4,3,16,19,40,95,136,321,588,1057,2240,3998,7848,15339,28464,
%T 56143,106788,204083,396704,755052,1457456,2806531,5377112,10382243,
%U 19947252,38382957,73996576,142311198,274283168,528438319,1017784016,1962451118,3781912684
%N Number of compositions of n, where the difference between the number of odd parts and the number of even parts is 2.
%C 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.
%H Alois P. Heinz, <a href="/A242500/b242500.txt">Table of n, a(n) for n = 2..1000</a>
%F 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
%Y Column k=2 of A242498.
%K nonn
%O 2,3
%A _Alois P. Heinz_, May 16 2014