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A112575 Chebyshev transform of the second kind of the Pell numbers. 3
0, 1, 2, 3, 6, 12, 22, 41, 78, 147, 276, 520, 980, 1845, 3474, 6543, 12322, 23204, 43698, 82293, 154974, 291847, 549608, 1035024, 1949160, 3670665, 6912610, 13017851, 24515262, 46167228, 86942286, 163730017, 308336942, 580661211, 1093503228, 2059289112 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The Chebyshev transform of the second kind maps the sequence with g.f. g(x) to the sequence with g.f. (1/(1+x^2))g(x/(1+x^2)).

LINKS

Table of n, a(n) for n=0..35.

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

FORMULA

G.f.: x/(1-2*x+x^2-2*x^3+x^4).

a(n) = Sum_{k=0..floor(n/2)} (-1)^k*C(n-k, k)*A000129(n-2k).

a(n) = Sum_{k=0..n} (-1)^((n-k)/2)*C((n+k)/2, k)*(1+(-1)^(n-k))*A000129(k)/2.

CROSSREFS

Cf. A000129.

Sequence in context: A047090 A185265 A018178 * A018079 A289920 A060985

Adjacent sequences:  A112572 A112573 A112574 * A112576 A112577 A112578

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Sep 14 2005

STATUS

approved

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Last modified November 29 18:41 EST 2021. Contains 349416 sequences. (Running on oeis4.)