A099492 A Chebyshev transform of the Padovan-Jacobsthal numbers.

1, 0, 0, 2, -1, -4, 5, 2, -16, 12, 27, -56, -3, 140, -144, -186, 547, -140, -1175, 1606, 1120, -5096, 2775, 9360, -16807, -4584, 45664, -38070, -69657, 167276, -11347, -393142, 450896, 467108, -1595725, 586584, 3235221, -4905692, -2556720, 14641550, -9572661, -25171740, 50306641, 6820750

Offset

0,4

Comments

A Chebyshev transform of A052947, which has g.f. 1/(1-x^2-2x^3). 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..43.

Index entries for linear recurrences with constant coefficients, signature (0,-2,2,-2,0,-1).

Formula

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

Mathematica

LinearRecurrence[{0, -2, 2, -2, 0, -1}, {1, 0, 0, 2, -1, -4}, 50] (* Harvey P. Dale, Dec 20 2015 *)

Crossrefs

Sequence in context: A038719 A125751 A210860 * A359708 A144203 A354699

Adjacent sequences: A099489 A099490 A099491 * A099493 A099494 A099495

Keyword

easy,sign

Author

Paul Barry, Oct 19 2004

Status

approved