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A135492 Number of ways to toss a coin n times and not get a run of five. 9
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,1,1,1).

FORMULA

a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4).

a(n) = 2*A000078(n+3).

G.f.: -2*x*(x+1)*(1+x^2)/(x^4+x^3+x^2+x-1). - Colin Barker, Jun 12 2012

MATHEMATICA

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 *)

PROG

(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

CROSSREFS

Cf. A135491, A135493.

Sequence in context: A164180 A164179 A027559 * A164191 A164193 A164192

Adjacent sequences:  A135489 A135490 A135491 * A135493 A135494 A135495

KEYWORD

nonn,easy

AUTHOR

James R FitzSimons (cherry(AT)getnet.net), Feb 07 2008

EXTENSIONS

Corrected and extended by Robert G. Wilson v, Feb 10 2008

STATUS

approved

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Last modified August 18 10:51 EDT 2017. Contains 290710 sequences.