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A094828
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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) = 1, s(2n) = 5.
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3
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1, 5, 20, 75, 274, 988, 3536, 12597, 44745, 158632, 561683, 1987154, 7026408, 24835744, 87763945, 310088381, 1095490524, 3869911659, 13670143618, 48287147300, 170561502896, 602454835293, 2127962632993, 7516243783216
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OFFSET
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2,2
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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))^(2*n) 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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LINKS
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FORMULA
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a(n) = (2/9)*Sum_{r=1..8} sin(r*Pi/9)*sin(5*r*Pi/9)*(2*cos(r*Pi/9))^(2*n).
a(n) = 7*a(n-1) - 15*a(n-2) + 10*a(n-3) - a(n-4).
G.f.: -x^2*(-1+2*x) / ( (x-1)*(x^3-9*x^2+6*x-1) ).
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MATHEMATICA
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LinearRecurrence[{7, -15, 10, -1}, {1, 5, 20, 75}, 30] (* Harvey P. Dale, Apr 27 2020 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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