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Search: id:A094832
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| A094832 |
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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) = 3, s(2n+1) = 4. |
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+0
2
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| 1, 3, 10, 34, 117, 406, 1417, 4965, 17443, 61390, 216318, 762841, 2691574, 9500193, 33539833, 118428835, 418214706, 1476968554, 5216307805, 18423344550, 65070265609, 229827800509, 811757757123, 2867166603766, 10127007608998
(list; graph; listen)
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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+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.
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FORMULA
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a(n+1)=3*a(n)+A094832(n-1) . - Philippe DELEHAM, Mar 18 2007
a(n)=(2/9)*Sum(r, 1, 8, Sin(r*Pi/3)Sin(4*r*Pi/9)(2Cos(r*Pi/9))^(2n)) a(n)=6a(n-1)-9a(n-2)+a(n-3) G.f.: (-1+3x-x^2)/(-1+6x-9x^2+x^3)
a(n)=A094833(n+2)-3*A094833(n+1). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 18 2007
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CROSSREFS
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Sequence in context: A007052 A048580 A059738 this_sequence A071725 A026016 A109263
Adjacent sequences: A094829 A094830 A094831 this_sequence A094833 A094834 A094835
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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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