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Search: id:A141016
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| A141016 |
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a(0)=0, a(1)=1, a(2)=2 a(3)=4; for n>3 a(n)=a(n-1)+2*a(n-2)+a(n-3)+a(n-4). |
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+0
1
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| 0, 1, 2, 4, 9, 20, 44, 97, 214, 472, 1041, 2296, 5064, 11169, 24634, 54332, 119833, 264300, 582932, 1285697, 2835694, 6254320, 13794337, 30424368, 67103056, 148000449, 326425266, 719953588, 1587907625, 3502240516, 7724434620
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OFFSET
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0,3
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COMMENT
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Central axis of triangle G(n, k): G(n,0)=G(n+1, n+1)=1, G(n+2, n+1)=2, G(n+3, n+1)=4, G(n+4, n+1)=8, G(n+5, k)=G(n+1, k-1)+G(n+1, k)+G(n+2, k)+G(n+3, k)+G(n+4, k) for k=1..(n+1).
Central axis of triangle G(n, k): G(n,n)=G(n+1, 0)=1, G(n+2, 1)=2, G(n+3, 2)=4, G(n+4, 3)=8, G(n+5, k)=G(n+1, k-3)+G(n+1, k-4)+G(n+2, k-3)+G(n+3, k-2)+G(n+4, k-1) for k=4..(n+4).
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FORMULA
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O.g.f.: x/(1-2x-x^3). a(n)=2a(n-1)+a(n-3). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 22 2008]
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MAPLE
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A141016:=proc(n) option remembrer: if n, =1 then n: else A141016(n-1)+2*A141016(n-2)+A141016(n-3)+A141016(n-4); fi; end.
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CROSSREFS
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Cf. A000129.
Sequence in context: A129988 A035530 A008998 this_sequence A024736 A024562 A087219
Adjacent sequences: A141013 A141014 A141015 this_sequence A141017 A141018 A141019
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KEYWORD
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nonn
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AUTHOR
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Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Jul 11 2008
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EXTENSIONS
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Terms from a(4) on corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 22 2008
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