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Search: id:A112575
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| A112575 |
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Chebyshev transform of the second kind of the Pell numbers. |
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+0
2
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| 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
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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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)).
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FORMULA
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G.f.: x/(1-2x+x^2-2x^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}.
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CROSSREFS
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Sequence in context: A082877 A047090 A018178 this_sequence A018079 A060985 A068012
Adjacent sequences: A112572 A112573 A112574 this_sequence A112576 A112577 A112578
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Sep 14 2005
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