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Search: id:A102900
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| A102900 |
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a(n)=3a(n-1)+4a(n-2), a(0)=a(1)=1. |
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+0
4
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| 1, 1, 7, 25, 103, 409, 1639, 6553, 26215, 104857, 419431, 1677721, 6710887, 26843545, 107374183, 429496729, 1717986919, 6871947673, 27487790695, 109951162777, 439804651111, 1759218604441, 7036874417767, 28147497671065
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Binomial transform of A102901.
Hankel transform is := 1,6,0,0,0,0,0,0,0,0,0,0,... [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 02 2008]
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REFERENCES
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Maria Paola Bonacina and Nachum Dershowitz, Canonical Inference for Implicational Systems, in Automated Reasoning, Lecture Notes in Computer Science, Volume 5195/2008, Springer-Verlag.
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FORMULA
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G.f.:(1-2x)/(1-3x-4x^2); a(n)=(2*4^n+3(-1)^n)/5; a(n)=ceiling(4^n/5)+floor(4^n/5)=(ceiling(4^n/5))^2-(floor(4^n/5))^2.
a(n)=sum{k=0..n, binomial(2n-k, 2k)2^k} - Paul Barry (pbarry(AT)wit.ie), Jan 20 2005
a(n) = upper left term in the 2 X 2 matrix [1,3; 2,2]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 14 2008
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CROSSREFS
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Cf. A001045, A046717.
Sequence in context: A138729 A035509 A141627 this_sequence A155271 A110240 A129791
Adjacent sequences: A102897 A102898 A102899 this_sequence A102901 A102902 A102903
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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), Jan 17 2005
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