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Search: id:A094831
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| A094831 |
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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) = 3, s(2n) = 3. |
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+0
1
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| 1, 2, 6, 19, 62, 207, 703, 2417, 8382, 29242, 102431, 359790, 1266103, 4460939, 15730497, 55500634, 195890270, 691566411, 2441886670, 8623112591, 30453261927, 107553444913, 379864424726, 1341658806066, 4738726458775
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OFFSET
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0,2
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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)=(2/9)*Sum(r, 1, 8, Sin(r*Pi/3)^2(2Cos(r*Pi/9))^(2n)) a(n)=6a(n-1)-9a(n-2)+a(n-3) G.f.: (-1+4x-3x^2)/(-1+6x-9x^2+x^3)
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CROSSREFS
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Sequence in context: A114627 A094817 A033565 this_sequence A033193 A071738 A026012
Adjacent sequences: A094828 A094829 A094830 this_sequence A094832 A094833 A094834
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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 13 2004
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