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Search: id:A094817
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| A094817 |
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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) = 3. |
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+0
1
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| 2, 6, 19, 62, 206, 692, 2340, 7944, 27032, 92112, 314128, 1071776, 3657824, 12485696, 42623040, 145512576, 496787840, 1696093440, 5790732544, 19770612224, 67500721664, 230461137920, 786842059776, 2686443866112
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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
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a(n)=(1/4)*Sum(r, 1, 7, Sin(3*r*Pi/8)^2(2Cos(r*Pi/8))^(2n)) a(n)= 6a(n-1)-10a(n-2)+4a(n-3), n>=4 G.f.: (-3+10x-6x^2)/(4(2x-1)(1-4x+2x^2))
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CROSSREFS
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Sequence in context: A148464 A148465 A148466 this_sequence A033565 A094831 A033193
Adjacent sequences: A094814 A094815 A094816 this_sequence A094818 A094819 A094820
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KEYWORD
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nonn
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AUTHOR
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Herbert Kociemba (kociemba(AT)t-online.de), Jun 12 2004
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