A099486 Expansion of x/((1 + x^2)*(1 - 4*x + x^2)).

0, 1, 4, 14, 52, 195, 728, 2716, 10136, 37829, 141180, 526890, 1966380, 7338631, 27388144, 102213944, 381467632, 1423656585, 5313158708, 19828978246, 74002754276, 276182038859, 1030725401160, 3846719565780, 14356152861960

Offset

0,3

Comments

A Chebyshev transform of the sequence 0,1,4,16,... which has g.f. x/(1-4x). The image of G(x) under the Chebyshev transform is (1/(1+x^2))*G(x/(1+x^2)).

Links

Table of n, a(n) for n=0..24.

Formula

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

a(n) = 4*a(n-1) - 2*a(n-2) + 4*a(n-3).

a(n) = Sum_{k=0..n} cos(Pi*(n-k)/2)*((2+sqrt(3))^k - (2-sqrt(3))^k)/(2*sqrt(3)).

a(n) = Sum_{k=0..floor(n/2)} binomial(n-k, k)*(-1)^n*(4^(n-2*k) - 0^(n-2*k))/4.

Crossrefs

Cf. A099487, A099488.

Sequence in context: A198279 A211307 A369577 * A047033 A017947 A244898

Adjacent sequences: A099483 A099484 A099485 * A099487 A099488 A099489

Keyword

easy,nonn

Author

Paul Barry, Oct 18 2004

Status

approved