A099495 A Chebyshev transform of Fib(n)^2.

0, 1, 1, 2, 6, 12, 25, 55, 118, 254, 548, 1179, 2539, 5470, 11780, 25370, 54641, 117681, 253452, 545866, 1175642, 2532005, 5453235, 11744748, 25294914, 54478198, 117330859, 252697979, 544241040, 1172143560, 2524470640, 5437006381

Offset

0,4

Comments

A Chebyshev transform of A007598, which has g.f. x(1-x)/((1+x)(1-3x+x^2)). 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..31.

Index entries for linear recurrences with constant coefficients, signature (2,-1,3,-1,2,-1).

Formula

G.f.: x(1-x+x^2)/((1+x+x^2)(1-3x+3x^2-3x^3+x^4)); a(n)=2a(n-1)-a(n-2)+3a(n-3)-a(n-4)+2a(n-5)-a(n-6); a(n)=sum{k=0..floor(n/2), binomial(n-k, k)(-1)^k*F(n-2k)^2}.

Mathematica

LinearRecurrence[{2, -1, 3, -1, 2, -1}, {0, 1, 1, 2, 6, 12}, 40] (* Harvey P. Dale, Nov 14 2021 *)

Crossrefs

Sequence in context: A128020 A140659 A238462 * A232164 A214663 A151385

Adjacent sequences: A099492 A099493 A099494 * A099496 A099497 A099498

Keyword

easy,nonn

Author

Paul Barry, Oct 19 2004

Status

approved