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A135492
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Number of ways to toss a coin n times and not get a run of five.
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9
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2, 4, 8, 16, 30, 58, 112, 216, 416, 802, 1546, 2980, 5744, 11072, 21342, 41138, 79296, 152848, 294624, 567906, 1094674, 2110052, 4067256, 7839888, 15111870, 29129066, 56148080, 108228904, 208617920, 402123970, 775118874, 1494089668, 2879950432
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4).
G.f.: -2*x*(x+1)*(1+x^2)/(x^4+x^3+x^2+x-1). - Colin Barker, Jun 12 2012
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MATHEMATICA
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a[n_] := a[n] = a[n - 1] + a[n - 2] + a[n - 3] + a[n - 4]; a[1] = 2; a[2] = 4; a[3] = 8; a[4] = 16; Array[a, 33] (* Robert G. Wilson v, Feb 10 2008 *)
LinearRecurrence[{1, 1, 1, 1}, {2, 4, 8, 16}, 25] (* G. C. Greubel, Oct 15 2016 *)
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PROG
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(PARI) a(n)=([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; 1, 1, 1, 1]^(n-1)*[2; 4; 8; 16])[1, 1] \\ Charles R Greathouse IV, Oct 17 2016
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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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James R FitzSimons (cherry(AT)getnet.net), Feb 07 2008
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EXTENSIONS
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STATUS
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approved
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