A242501 - OEIS

%I #7 May 20 2014 02:41:17

%S 1,0,3,5,6,25,31,75,162,259,609,1106,2122,4410,8076,16197,31527,59961,

%T 118844,227700,441507,860860,1654731,3218501,6226818,12027405,

%U 23337471,45082050,87258876,168935018,326536646,632132760,1222716653,2364969824,4576680195

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

%C 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.

%H Alois P. Heinz, <a href="/A242501/b242501.txt">Table of n, a(n) for n = 3..1000</a>

%F 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

%Y Column k=3 of A242498.

%K nonn

%O 3,3

%A _Alois P. Heinz_, May 16 2014