A100052 A Chebyshev transform of the odd numbers.

1, 3, 3, -2, -9, -9, 2, 15, 15, -2, -21, -21, 2, 27, 27, -2, -33, -33, 2, 39, 39, -2, -45, -45, 2, 51, 51, -2, -57, -57, 2, 63, 63, -2, -69, -69, 2, 75, 75, -2, -81, -81, 2, 87, 87, -2, -93, -93, 2, 99, 99, -2, -105, -105, 2, 111, 111, -2, -117, -117

Offset

0,2

Comments

A Chebyshev transform of A005408: 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

Table of n, a(n) for n=0..59.

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

Formula

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

Mathematica

LinearRecurrence[{2, -3, 2, -1}, {1, 3, 3, -2, -9}, 80] (* Harvey P. Dale, Aug 18 2016 *)

Crossrefs

Sequence in context: A248569 A214101 A286952 * A128504 A193822 A202699

Adjacent sequences: A100049 A100050 A100051 * A100053 A100054 A100055

Keyword

easy,sign

Author

Paul Barry, Oct 31 2004

Status

approved