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A094826
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Number of (s(0), s(1), ..., s(2n)) such that 0 < s(i) < 9 and |s(i) - s(i-1)| = 1 for i = 1,2,....,2n, s(0) = 1, s(2n) = 3.
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0
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1, 3, 9, 28, 90, 297, 1000, 3417, 11799, 41041, 143472, 503262, 1769365, 6230304, 21960801, 77461435, 273351705, 964918116, 3406804786, 12029917377, 42483179304, 150036624217, 529901048943, 1871559855009, 6610286313784
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| In general a(n)= (2/m)*Sum(r,1,m-1,Sin(r*j*Pi/m)Sin(r*k*Pi/m)(2Cos(r*Pi/m))^(2n)) counts (s(0), s(1), ..., s(2n)) such that 0 < s(i) < m and |s(i)-s(i-1)| = 1 for i = 1,2,....,2n, s(0) = j, s(2n) = k.
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FORMULA
| a(n)=(2/9)*Sum(r, 1, 8, Sin(r*Pi/9)Sin(3*r*Pi/9)(2Cos(r*Pi/9))^(2n)) a(n)=6a(n-1)-9a(n-2)+a(n-3) and also a(n)=7a(n-1)-15a(n-2)+10a(n-3)-a(n-4) G.f.: x(-1+3x)/(-1+6x-9x^2+x^3)
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CROSSREFS
| Sequence in context: A007822 A094164 A094803 * A033190 A071724 A000245
Adjacent sequences: A094823 A094824 A094825 * A094827 A094828 A094829
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KEYWORD
| nonn
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AUTHOR
| Herbert Kociemba (kociemba(AT)t-online.de), Jun 13 2004
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