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Search: id:A007971
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| A007971 |
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INVERT transform of central trinomial coefficients (A002426). |
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+0
7
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| 0, 1, 2, 2, 4, 8, 18, 42, 102, 254, 646, 1670, 4376, 11596, 31022, 83670, 227268, 621144, 1706934, 4713558, 13072764, 36398568, 101704038, 285095118, 801526446, 2259520830, 6385455594, 18086805002, 51339636952, 146015545604
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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For n>1, a(n) = 2(A005043(n-1)+A005043(n-2)). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Jul 06 2003
Number of paths of a walk on the integers, allowing steps of size 0, +1, and -1, which return to the starting point for the first time at time n. [From David P. Sanders (dps(AT)fciencias.unam.mx), May 04 2009]
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FORMULA
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A002426(n) = Sum_{i=1..n} a(i)*A002426(n-i), n>0.
G.f.: 1-sqrt(1-2*x-3*x^2).
a(0)=0, a(1)=1, a(2)=2, then a(n)= (1/2) *(a(1)*a(n-1)+a(2)*a(n-2)+....+a(n-1)*a(1)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 24 2003
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CROSSREFS
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Cf. A002426. A001006(n)=A007971(n+2)/2.
Cf. A025227.
Adjacent sequences: A007968 A007969 A007970 this_sequence A007972 A007973 A007974
Sequence in context: A108774 A063402 A139800 this_sequence A126068 A005702 A095335
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KEYWORD
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nonn
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AUTHOR
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David Dumas (dumas(AT)TCNJ.EDU)
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