A109222 Row sums of a triangle related to the Fibonacci polynomials.

1, 2, 3, 6, 11, 21, 40, 76, 145, 276, 526, 1002, 1909, 3637, 6929, 13201, 25150, 47915, 91286, 173915, 331337, 631252, 1202640, 2291229, 4365172, 8316378, 15844082, 30185609, 57508601, 109563441, 208736561, 397677834, 757642355, 1443434582

Offset: 0

Author

Paul Barry, Jun 22 2005

Keywords

• easy
• nonn

Comments

Row sums of A109221.

The Kn4 sums, see A180662, of triangle A065941 equal the terms of this sequence a(n) while the Kn4 sums of triangle A194005 equal a(n+1)-1. - Johannes W. Meijer, Aug 14 2011

Links

• Index entries for linear recurrences with constant coefficients, signature (1,2,0,-1).

Programs

Maple

A109222 := proc(n): add(binomial(floor((2*n-k)/2)+n-k, 2*n-2*k), k=0..n) end:  seq(A109222(n), n=0..33); # Johannes W. Meijer, Aug 14 2011

Formula

G.f.: (1 + x - x^2 - x^3)/(1 - x - 2x^2 + x^4);

a(n) = a(n-1) + 2a(n-2) - a(n-4);

a(n) = Sum_{k=0..n} binomial(floor((2n-k)/2)+n-k, 2n-2k).