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A135491 Number of ways to toss a coin n times and not get a run of four. 17
1, 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; text; internal format)
OFFSET
0,2
LINKS
Elena Barcucci, Antonio Bernini, Stefano Bilotta, Renzo Pinzani, Non-overlapping matrices, arXiv:1601.07723 [cs.DM], 2016. See column 2 of Table 2 p. 11.
Elena Barcucci, Antonio Bernini, Stefano Bilotta and Renzo Pinzani, Non-overlapping matrices, Theoretical Computer Science, Vol. 658, Part A (2017), 36-45.
B. Chaffin, J. P. Linderman, N. J. A. Sloane and Allan Wilks, On Curling Numbers of Integer Sequences, arXiv:1212.6102 [math.CO], 2012-2013.
B. Chaffin, J. P. Linderman, N. J. A. Sloane and Allan Wilks, On Curling Numbers of Integer Sequences, Journal of Integer Sequences, Vol. 16 (2013), Article 13.4.3.
Emrah Kılıç, Talha Arıkan, Evaluation of Hessenberg determinants with recursive entries: generating function approach, Filomat (2017) Vol. 31, Issue 15, pp. 4945-4962.
A. V. Zharkova, Inaccesible States in Dynamic Systems Associated with Paths and Cycles, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 11 (2011), 116-122.
FORMULA
a(n) = 2*A000073(n+2) for n > 0.
a(n) = a(n-1) + a(n-2) + a(n-3) for n > 3.
G.f.: -(x+1)*(x^2+1)/(x^3+x^2+x-1).
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. See A058265. - N. J. A. Sloane, Jan 06 2010
G.f.: (1-x^4)/(1-2*x+x^4) and generally to "not get a run of k" (1-x^k)/(1-2*x+x^k). - Geoffrey Critzer, Feb 01 2012
G.f.: Q(0)/x^2 - 2/x- 1/x^2, where Q(k) = 1 + (1+x)*x^2 + (2*k+3)*x - x*(2*k+1 +x+x^2)/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, Oct 04 2013
a(n) = A000213(n+3) - A000213(n+2), n>=1. - Peter M. Chema, Jan 11 2017.
MATHEMATICA
LinearRecurrence[{1, 1, 1}, {1, 2, 4, 8}, 36] (* Vladimir Joseph Stephan Orlovsky, Jul 23 2011; first term 1 added by Georg Fischer, Apr 02 2019 *)
PROG
(PARI) Vec(1-2*x*(1+x+x^2)/(-1+x+x^2+x^3) + O(x^100)) \\ Altug Alkan, Dec 10 2015
CROSSREFS
Cf. A000073. Column 2 of A265624. Cf. A135492, A135493, A000213, A058265.
Sequence in context: A117633 A308148 A273154 * A164154 A164156 A257934
KEYWORD
nonn,easy
AUTHOR
James R FitzSimons (cherry(AT)getnet.net), Feb 07 2008
EXTENSIONS
More terms from Robert G. Wilson v, Feb 10 2008
a(0)=1 prepended by Alois P. Heinz, Dec 10 2015
STATUS
approved

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Last modified June 22 16:03 EDT 2024. Contains 373590 sequences. (Running on oeis4.)