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A135491
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Number of ways to toss a coin n times and not get a run of four.
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6
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2, 4, 8, 14, 26, 48, 88, 162, 298, 548, 1008, 1854, 3410, 6272, 11536, 21218, 39026, 71780, 132024, 242830, 446634, 821488, 1510952, 2779074, 5111514, 9401540, 17292128, 31805182, 58498850, 107596160, 197900192, 363995202, 669491554, 1231386948, 2264873704
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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FORMULA
| a(n)=a(n-1)+a(n-2)+a(n-3)
a(n) = nearest integer to b*c^n, where b = 1.2368... and c = 1.839286755... is the real root of x^3-x^2-x-1 = 0. - N. J. A. Sloane, Jan 06 2010
G.f.: (1-x^4)/(1-2x+x^4) and generally to "not get a run of k" (1-x^k)/(1-2x+x^k). - Geoffrey Critzer, Feb 01 2012
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MATHEMATICA
| a[n_] := a[n] = a[n - 1] + a[n - 2] + a[n - 3]; a[1] = 2; a[2] = 4; a[3] = 8; Array[a, 33] - Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 10 2008
LinearRecurrence[{1, 1, 1}, {2, 4, 8}, 50] (* From Vladimir Joseph Stephan Orlovsky, Jul 23 2011 *)
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CROSSREFS
| a(n)=2*A000073(n+2). Cf. A135492, A135493.
Sequence in context: A130708 A054193 A117633 * A164154 A164156 A164155
Adjacent sequences: A135488 A135489 A135490 * A135492 A135493 A135494
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KEYWORD
| nonn,changed
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AUTHOR
| James R FitzSimons (cherry(AT)getnet.net), Feb 07 2008
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 10 2008
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