OFFSET
0,6
COMMENTS
A Chebyshev transform of the Padovan numbers A000931(n+3): if A(x) is the g.f. of a sequence, map it to ((1-x^2)/(1+x^2))A(x/(1+x^2)).
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,-2,1,-2,0,-1).
FORMULA
G.f.: (1-x^2)*(1+x^2)^2/(1+2*x^2-x^3+2*x^4+x^6).
a(n) = -2*a(n-2) +a(n-3) -2*a(n-4) -a(n-6).
a(n) = n*Sum_{k=0..floor(n/2)} (-1)^k*binomial(n-k,k)*A000931(n-2*k+3)/(n-k).
MATHEMATICA
LinearRecurrence[{0, -2, 1, -2, 0, -1}, {1, 0, -1, 1, -1, -3, 3}, 50] (* G. C. Greubel, Aug 08 2017 *)
PROG
(PARI) x='x+O('x^50); Vec((1-x^2)*(1+x^2)^2/(1+2*x^2-x^3+2*x^4+x^6)) \\ G. C. Greubel, Aug 08 2017
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Paul Barry, Oct 31 2004
STATUS
approved