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Search: id:A033191
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| A033191 |
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Binomial transform of [ 1, 0, 1, 1, 3, 6, 15, 36, 91, 231, 595,... ], which is essentially binomial(fibonacci(k) + 1, 2). |
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+0
5
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| 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4861, 16778, 58598, 206516, 732825, 2613834, 9358677, 33602822, 120902914, 435668420, 1571649221, 5674201118, 20497829133, 74079051906, 267803779710, 968355724724
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Number of (s(0), s(1), ..., s(2n)) such that 0 < s(i) < 10 and |s(i) - s(i-1)| = 1 for i = 1,2,....,2n, s(0) = 1, s(2n) = 1. - Herbert Kociemba (kociemba(AT)t-online.de), Jun 14 2004
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FORMULA
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G.f.: (1-7x+15x^2-10x^3+x^4)/(1-8x+21x^2-20x^3+5x^4). - Ralf Stephan (ralf(AT)ark.in-berlin.de), May 13 2003
a(n)=(1/5)*Sum(r, 1, 9, Sin(r*Pi/10)^2(2Cos(r*Pi/10))^(2n)), n>=1 a(n)=8a(n-1)-21a(n-2)+20a(n-3)-5a(n-4), n>=5 - Herbert Kociemba (kociemba(AT)t-online.de), Jun 14 2004
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CROSSREFS
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Cf. A033192.
Sequence in context: A080938 A054394 A036769 this_sequence A000108 A115140 A120588
Adjacent sequences: A033188 A033189 A033190 this_sequence A033192 A033193 A033194
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KEYWORD
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nonn
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AUTHOR
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Simon Norton (simon(AT)dpmms.cam.ac.uk)
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