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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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5
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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
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OFFSET
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0,2
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COMMENTS
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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)*(2*cos(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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LINKS
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FORMULA
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a(n) = (2/9)*Sum_{r=1..8} sin(r*Pi/3)*sin(4*r*Pi/9)*(2*cos(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).
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MATHEMATICA
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LinearRecurrence[{6, -9, 1}, {1, 3, 10}, 30] (* Harvey P. Dale, May 18 2011 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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