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A054881
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Number of walks of length n along the edges of an octahedron starting and ending at a vertex and also ( with a(0)=0 ) between two opposite vertices.
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11
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1, 0, 4, 8, 48, 160, 704, 2688, 11008, 43520, 175104, 698368, 2797568, 11182080, 44744704, 178946048, 715849728, 2863267840, 11453333504, 45812809728, 183252287488, 733007052800, 2932032405504, 11728121233408
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = 4*A003683(n-1) + 0^n/2, n >= 0.
a(n) = (4^n + (-1)^n*2^(n+1) + 3*0^n)/6.
G.f.: (1/6)*(3 + 2/(1+2*x) + 1/(1-4*x)).
G.f.: (1-2*x-4*x^2)/((1+2*x)*(1-4*x)).
a(n) = 8*A246036(n-3) + 0^n/2, n >= 0. (End)
E.g.f.: (1/6)*(exp(4*x) + 2*exp(-2*x) + 3). - G. C. Greubel, Feb 06 2023
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MATHEMATICA
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CoefficientList[Series[(1-2*x-4*x^2)/((1+2x)*(1-4x)), {x, 0, 40}], x] (* L. Edson Jeffery, Apr 22 2015 *)
LinearRecurrence[{2, 8}, {1, 0, 4}, 41] (* G. C. Greubel, Feb 06 2023 *)
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PROG
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(Magma) [(4^n+(-1)^n*2^(n+1)+3*0^n)/6: n in [0..30]]; // Vincenzo Librandi, Apr 23 2015
(SageMath) [(4^n + (-1)^n*2^(n+1) + 3*0^n)/6 for n in range(31)] # G. C. Greubel, Feb 06 2023
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CROSSREFS
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KEYWORD
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nonn,walk,easy
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AUTHOR
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Paolo Dominici (pl.dm(AT)libero.it), May 23 2000
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STATUS
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approved
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