A099491 A Chebyshev transform of Padovan numbers.

1, 0, 0, 1, -1, -2, 2, 1, -4, 3, 6, -10, -3, 19, -12, -24, 43, 8, -83, 56, 100, -187, -21, 354, -262, -411, 820, 39, -1506, 1210, 1673, -3593, 56, 6400, -5545, -6768, 15705, -1216, -27144, 25273, 27207, -68490, 9442, 114857, -114644, -108565, 298054, -58738, -484827, 517803, 429452, -1294392, 330499

Offset

0,6

Comments

A Chebyshev transform of A000931(n+3), which has g.f. 1/(1-x^2-x^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..52.

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

Formula

G.f.: (1+x^2)^2/(1+2x^2-x^3+2x^4+x^6); a(n)=-2a(n-2)+a(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)}}.

Crossrefs

Cf. A099492.

Sequence in context: A263203 A023616 A276477 * A322082 A334770 A274622

Adjacent sequences: A099488 A099489 A099490 * A099492 A099493 A099494

Keyword

easy,sign

Author

Paul Barry, Oct 19 2004

Status

approved