A099488 Expansion of (1-x)^2/((1+x^2)(1-4x+x^2)).

1, 2, 7, 28, 105, 390, 1455, 5432, 20273, 75658, 282359, 1053780, 3932761, 14677262, 54776287, 204427888, 762935265, 2847313170, 10626317415, 39657956492, 148005508553, 552364077718, 2061450802319, 7693439131560, 28712305723921

Offset

0,2

Comments

A Chebyshev transform of the sequence A081294 which has with g.f. (1-2x)/(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.

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

Formula

a(n)=4a(n-1)-2a(n-2)+4a(n-3); a(n)=sum{k=0..n, (0^k-2sin(pi*k/2))((2+sqrt(3))^(n-k+1)-(2-sqrt(3))^(n-k+1))/(2*sqrt(3))}; a(n)=sum{k=0..n, (0^k-2sin(pi*k/2))A001353(n-k)}; a(n)=sum{k=0..floor(n/2), binomial(n-k, k)(-1)^k*(4^(n-2k)+0^(n-2k))/2}.

Mathematica

CoefficientList[Series[(1-x)^2/((1+x^2)(1-4x+x^2)), {x, 0, 30}], x] (* or *) LinearRecurrence[{4, -2, 4, -1}, {1, 2, 7, 28}, 30] (* Harvey P. Dale, Jun 23 2015 *)

Crossrefs

Cf. A099486, A099487.

Sequence in context: A349329 A048504 A092465 * A289607 A068944 A215143

Adjacent sequences: A099485 A099486 A099487 * A099489 A099490 A099491

Keyword

easy,nonn

Author

Paul Barry, Oct 18 2004

Status

approved