A099626 A transform of the Pell numbers.

0, 1, 2, 7, 18, 52, 142, 397, 1098, 3051, 8460, 23480, 65140, 180749, 501498, 1391483, 3860822, 10712348, 29722698, 82469313, 228821202, 634892599, 1761587480, 4887741040, 13561638120, 37628431801, 104404708402, 289683694927

Offset

0,3

Comments

A modified Chebyshev transform of A000129. Under this transform, the g.f. G(x) is mapped to (1/(1-x^2))G(x/(1-x^2)).

Links

Table of n, a(n) for n=0..27.

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

Formula

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

Crossrefs

Sequence in context: A094976 A280598 A006869 * A261331 A046672 A046866

Adjacent sequences: A099623 A099624 A099625 * A099627 A099628 A099629

Keyword

easy,nonn

Author

Paul Barry, Oct 25 2004

Status

approved