A099487 Expansion of (1-3x+x^2)/((1+x^2)(1-4x+x^2)).

1, 1, 3, 14, 53, 195, 727, 2716, 10137, 37829, 141179, 526890, 1966381, 7338631, 27388143, 102213944, 381467633, 1423656585, 5313158707, 19828978246, 74002754277, 276182038859, 1030725401159, 3846719565780, 14356152861961

Offset: 0

Author

Paul Barry, Oct 18 2004

Keywords

• easy
• nonn

Comments

A Chebyshev transform of the sequence 1,1,4,16.. which has with g.f. (1-3x)/(1-4x). The image of G(x) under the Chebyshev transform is (1/(1+x^2))G(x/(1+x^2)).

Links

• Index entries for linear recurrences with constant coefficients, signature (4,-2,4,-1).

Crossrefs

Cf. A099486, A099488.

Formula

a(n)=4a(n-1)-2a(n-2)+4a(n-3); a(n)=sum{k=0..floor(n/2), C(n-k, k)(-1)^n*(4^(n-2k)+3*0^(n-2k))/4}.