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

0,2

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

Table of n, a(n) for n=0..33.

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

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).

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

Crossrefs

Sequence in context: A132832 A316796 A079116 * A191789 A371790 A306575

Adjacent sequences: A109219 A109220 A109221 * A109223 A109224 A109225

Keyword

easy,nonn

Author

Paul Barry, Jun 22 2005

Status

approved