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A094828
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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) = 5.
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0
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1, 5, 20, 75, 274, 988, 3536, 12597, 44745, 158632, 561683, 1987154, 7026408, 24835744, 87763945, 310088381, 1095490524, 3869911659, 13670143618, 48287147300, 170561502896, 602454835293, 2127962632993, 7516243783216
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,2
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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(5*r*Pi/9)(2Cos(r*Pi/9))^(2n)) a(n)=7a(n-1)-15a(n-2)+10a(n-3)-a(n-4) G.f.: x^2(-1+2x)/(-1+7x-15x^2+10x^3-x^4)
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CROSSREFS
| Sequence in context: A026639 A022633 A092490 * A030191 A093131 A000344
Adjacent sequences: A094825 A094826 A094827 * A094829 A094830 A094831
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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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