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A094788
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Number of (s(0), s(1), ..., s(2n+1)) such that 0 < s(i) < 10 and |s(i) - s(i-1)| = 1 for i = 1,2,...,2n+1, s(0) = 1, s(2n+1) = 6.
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4
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1, 6, 27, 110, 428, 1624, 6069, 22458, 82555, 302082, 1101816, 4009616, 14567657, 52865230, 191684283, 694609494, 2515972324, 9110338728, 32981059485, 119377761602, 432046756571, 1563510554986, 5657752486512, 20472344560800
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OFFSET
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2,2
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COMMENTS
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LINKS
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FORMULA
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a(n) = (1/5)*Sum_{r=1..9} sin(r*Pi/10)*sin(3*r*Pi/5)*(2*cos(r*Pi/10))^(2*n+1).
a(n) = 8*a(n-1) - 21*a(n-2) + 20*a(n-3) - 5*a(n-4).
G.f.: -x^2*(-1+2*x) / ( (x^2-3*x+1)*(5*x^2-5*x+1) ).
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MATHEMATICA
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Drop[CoefficientList[Series[-x^2*(-1 + 2 x)/((x^2 - 3 x + 1) (5 x^2 - 5 x + 1)), {x, 0, 25}], x], 2] (* Michael De Vlieger, Aug 04 2021 *)
LinearRecurrence[{8, -21, 20, -5}, {1, 6, 27, 110}, 30] (* Harvey P. Dale, Aug 31 2021 *)
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PROG
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(PARI) Vec(x^2*(1-2*x)/(1-8*x+21*x^2-20*x^3+5*x^4)+O(x^66)) /* Joerg Arndt, Mar 29 2013 */
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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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