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A094827
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Number of (s(0), s(1), ..., s(2n+1)) such that 0 < s(i) < 9 and |s(i) - s(i-1)| = 1 for i = 1,2,....,2n+1, s(0) = 1, s(2n+1) = 4.
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0
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1, 4, 14, 48, 165, 571, 1988, 6953, 24396, 85786, 302104, 1064945, 3756519, 13256712, 46796545, 165225380, 583440086, 2060408640, 7276716445, 25700060995, 90770326604, 320598127113, 1132355884236, 3999522488002
(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+1)) counts (s(0), s(1), ..., s(2n+1)) such that 0 < s(i) < m and |s(i)-s(i-1)| = 1 for i = 1,2,....,2n+1, s(0) = j, s(2n+1) = k.
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FORMULA
| a(n)=(2/9)*Sum(r, 1, 8, Sin(r*Pi/9)Sin(4*r*Pi/9)(2Cos(r*Pi/9))^(2n+1)) a(n)=7a(n-1)-15a(n-2)+10a(n-3)-a(n-4) G.f.: x(-1+3x-x^2)/(-1+7x-15x^2+10x^3-x^4)
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CROSSREFS
| Sequence in context: A007070 A204089 A092489 * A094667 A002057 A099376
Adjacent sequences: A094824 A094825 A094826 * A094828 A094829 A094830
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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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