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A094821
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Number of (s(0), s(1), ..., s(2n)) such that 0 < s(i) < 8 and |s(i) - s(i-1)| = 1 for i = 1,2,....,2n, s(0) = 3, s(2n) = 5.
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0
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1, 4, 15, 54, 190, 660, 2276, 7816, 26776, 91600, 313104, 1069728, 3653728, 12477504, 42606656, 145479808, 496722304, 1695962368, 5790470400, 19770087936, 67499673088, 230459040768, 786837865472, 2686435477504
(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)=(1/4)*Sum(r, 1, 7, Sin(3*r*Pi/8)Sin(5*r*Pi/8)(2Cos(r*Pi/8))^(2n)) a(n)= 6a(n-1)-10a(n-2)+4a(n-3), n>=4 G.f.: (1-2x+2x^2)/(4(-1+2x)(-1+4x-2x^2))
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CROSSREFS
| Sequence in context: A164619 A090326 A006234 * A071723 A001559 A002311
Adjacent sequences: A094818 A094819 A094820 * A094822 A094823 A094824
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KEYWORD
| nonn
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AUTHOR
| Herbert Kociemba (kociemba(AT)t-online.de), Jun 12 2004
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