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Search: id:A112577
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| A112577 |
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A Chebyshev-related transform of the Jacobsthal numbers. |
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+0
1
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| 0, 1, 1, 5, 8, 26, 52, 143, 317, 811, 1884, 4668, 11076, 27053, 64805, 157273, 378364, 915598, 2206976, 5333731, 12867673, 31080023, 75010008, 181128696, 437221032, 1055645785, 2548391209, 6152624621, 14853322640, 35859784130, 86572058860
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Transform of the Jacobsthal numbers by the Chebyshev related transform which maps g(x)->(1/(1-x^2))g(x/(1-x^2)).
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FORMULA
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G.f.: x/(1-x-4x^2+x^3+x^4); a(n)=sum{k=0..floor(n/2), C(n-k, k)*A001045(n-2k)}; a(n)=sum{k=0..n, C((n+k)/2, k)*(1+(-1)^(n-k))*A001045(k)/2}; a(n)=sum{k=0..n, (-1)^k*F(k+1)*A000129(n-k+1)}.
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CROSSREFS
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Adjacent sequences: A112574 A112575 A112576 this_sequence A112578 A112579 A112580
Sequence in context: A038250 A067973 A101584 this_sequence A026539 A126700 A076593
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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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