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Search: id:A085350
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| 1, 5, 23, 101, 431, 1805, 7463, 30581, 124511, 504605, 2038103, 8211461, 33022991, 132623405, 532087943, 2133134741, 8546887871, 34230598205, 137051532983, 548593552421, 2195536471151, 8785632669005, 35152991029223
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OFFSET
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0,2
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COMMENT
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Binomial transform is A085351.
a(n) mod 10=period 4:repeat 1,5,3,1=A132400. [From Paul Curtz (bpcrtz(AT)free.fr), Nov 13 2009]
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FORMULA
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G.f.: (1-2x)/((1-3x)(1-4x)); e.g.f.: 2exp(4x)-exp(3x); a(n)=2*4^n-3^n.
a(n)=4a(n-1)+9a(n-2)-36a(n-3); a(n)=4a(n-1)+3^(n-1), both like A005061 (note for A005061 dual formula a(n)=3a(n-1)+4^(n-1)=3a(n-1)+A000302)). a(n)=3a(n-1)+2^(2n+1)=3a(n-1)+A004171. a(n)=A085350=A005061+A000302. (b(n)=mix A005061 , A085350)=0,1,1,5,7,23,=differences of (A167762=0,0,1,2,7,14,37,); b(n) differences=A167784. [From Paul Curtz (bpcrtz(AT)free.fr), Nov 13 2009]
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CROSSREFS
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a(n-1) = A080643(n)/2 = A081674(n+1)-A081674(n).
Sequence in context: A077277 A073682 A034958 this_sequence A113443 A124999 A120902
Adjacent sequences: A085347 A085348 A085349 this_sequence A085351 A085352 A085353
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KEYWORD
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easy,nonn,new
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Jun 24 2003
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