A117353 Expansion of (1-x)/(1-3x+x^2+4x^3-4x^4).

1, 2, 5, 9, 18, 33, 65, 126, 253, 505, 1018, 2041, 4097, 8198, 16405, 32793, 65570, 131089, 262145, 524238, 1048493, 2097017, 4194186, 8388521, 16777281, 33554646, 67109317, 134218265, 268436018, 536871105, 1073741505, 2147482398

Offset: 0

Author

Paul Barry, Mar 09 2006

Keywords

• easy
• nonn

Comments

Diagonal sums of number triangle A117352.

Links

• Index entries for linear recurrences with constant coefficients, signature (3,-1,-4,4).

Formula

G.f.: (1-x)/((1-2x)(1-x-x^2+2x^3)); a(n)=3a(n-1)-a(n-2)-4a(n-3)+4a(n-4); a(n)=sum{k=0..floor(n/2), sum{j=0..n-2k, C(j-k,j)C(n-2k,j)}}.