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A100048 A Chebyshev transform of the Pell numbers. 4
0, 1, 2, 2, 4, 9, 16, 29, 56, 106, 198, 373, 704, 1325, 2494, 4698, 8848, 16661, 31376, 59089, 111276, 209554, 394634, 743177, 1399552, 2635641, 4963450, 9347186, 17602652, 33149377, 62427024, 117562789, 221394656, 416931194, 785166286 (list; graph; refs; listen; history; internal format)
OFFSET

0,3

COMMENTS

A Chebyshev transform of the Pell numbers A000129: if A(x) is the g.f. of a sequence, map it to ((1-x^2)/(1+x^2))A(x/(1+x^2)).

FORMULA

G.f.: x(1-x^2)/(1-2x+x^2-2x^3+x^4); a(n)=2a(n-1)-a(n-2)+2a(n-3)-a(n-4); a(n)=n*sum{k=0..floor(n/2), (-1)^k*binomial(n-k, k)A000129(n-2k)/(n-k)}.

CROSSREFS

Cf. A099443, A011655, A100047.

Sequence in context: A054231 A054230 A054232 * A052935 A166022 A052925

Adjacent sequences:  A100045 A100046 A100047 * A100049 A100050 A100051

KEYWORD

easy,nonn

AUTHOR

Paul Barry (pbarry(AT)wit.ie), Oct 31 2004

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Last modified February 17 06:27 EST 2012. Contains 205998 sequences.