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Search: id:A094829
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| A094829 |
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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) = 6. |
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| 1, 6, 27, 109, 417, 1548, 5644, 20349, 72846, 259579, 922209, 3269889, 11579032, 40967400, 144863001, 512050438, 1809503019, 6393427173, 22587086305, 79791176292, 281856708180, 995606748757, 3516721295214
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OFFSET
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2,2
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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+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.
a(n) = 6*a(n-1) - 9*a(n-2) + a(n-3). Example: a(7) = 1548 = 6*a(6) - 9*a(5) + a(4) = 6*417 - 9*109 + 27. - Gary W. Adamson (qntmpkt(AT)yahoo.com), May 29 2008
a(n)/a(n-1) tends to 3.53208888...; = (2 + 2*Cos 2Pi/9). - Gary W. Adamson (qntmpkt(AT)yahoo.com), May 29 2008
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FORMULA
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a(n)=(2/9)*Sum(r, 1, 8, Sin(r*Pi/9)Sin(2*r*Pi/3)(2Cos(r*Pi/9))^(2n)) a(n)=6a(n-1)-9a(n-2)+a(n-3) G.f.: x^2/(1-6x+9x^2-x^3)
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CROSSREFS
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Adjacent sequences: A094826 A094827 A094828 this_sequence A094830 A094831 A094832
Sequence in context: A119852 A027471 A037695 this_sequence A055145 A037604 A022634
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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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