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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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3
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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; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| 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]
a(n)+a(n+1)=2^(2*n+1)=A004171(n).
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REFERENCES
| 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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LINKS
| Index entries for sequences related to linear recurrences with constant coefficients, signature (3,4).
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FORMULA
| 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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MATHEMATICA
| a[n_]:=(MatrixPower[{{2, 2}, {3, 1}}, n].{{2}, {1}})[[2, 1]]; Table[a[n], {n, 0, 40}] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 20 2010]
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CROSSREFS
| Cf. A001045, A046717.
Sequence in context: A138729 A035509 A141627 * A155271 A200152 A110240
Adjacent sequences: A102897 A102898 A102899 * A102901 A102902 A102903
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Jan 17 2005
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