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
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
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Oct 19 2004
STATUS
approved