login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A135491 Number of ways to toss a coin n times and not get a run of four. 16
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

G. C. Greubel, Table of n, a(n) for n = 0..1000

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.

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.

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

FORMULA

a(n) = 2*A000073(n+2)

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

G.f.: 1-2*x*(1+x+x^2) / ( -1+x+x^2+x^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)/(1-2*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

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, Feb 10 2008 *)

LinearRecurrence[{1, 1, 1}, {2, 4, 8}, 50] (* Vladimir Joseph Stephan Orlovsky, Jul 23 2011 *)

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 .

Sequence in context: A054193 A117633 A273154 * A164154 A164156 A257934

Adjacent sequences:  A135488 A135489 A135490 * A135492 A135493 A135494

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified March 26 07:24 EDT 2017. Contains 284111 sequences.