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A050232 a(n) is the number of n-tosses having a run of 4 or more heads for a fair coin (i.e., probability is a(n)/2^n). 8
0, 0, 0, 1, 3, 8, 20, 48, 111, 251, 558, 1224, 2656, 5713, 12199, 25888, 54648, 114832, 240335, 501239, 1042126, 2160676, 4468664, 9221281, 18989899, 39034824, 80103276, 164126496, 335808927, 686182387, 1400438814 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

a(n-1) is the number of compositions of n with at least one part >= 5. - Joerg Arndt, Aug 06 2012

REFERENCES

Feller, W. An Introduction to Probability Theory and Its Application, Vol. 1, 2nd ed. New York: Wiley, p. 300, 1968.

LINKS

T. D. Noe, Table of n, a(n) for n = 1..300

Simon Cowell, A Formula for the Reliability of a d-dimensional Consecutive-k-out-of-n:F System, arXiv preprint arXiv:1506.03580 [math.CO], 2015.

T. Langley, J. Liese, J. Remmel, Generating Functions for Wilf Equivalence Under Generalized Factor Order , J. Int. Seq. 14 (2011) # 11.4.2

Eric Weisstein's World of Mathematics, Run

Index entries for linear recurrences with constant coefficients, signature (3, -1, -1, -1, -2).

FORMULA

a(n) = 2^n - tetranacci(n+4), see A000078. - Vladeta Jovovic, Feb 23 2003

G.f.: x^4/((1-2*x)*(1-x-x^2-x^3-x^4)) - Geoffrey Critzer, Jan 29 2009

MATHEMATICA

Flatten[With[{tetrnos=LinearRecurrence[{1, 1, 1, 1}, {0, 1, 1, 2}, 50]}, Table[ 2^n- Take[tetrnos, {n+3}], {n, 40}]]] (* Harvey P. Dale, Dec 02 2011 *)

LinearRecurrence[{3, -1, -1, -1, -2}, {0, 0, 0, 1, 3}, 31] (* Ray Chandler, Aug 03 2015 *)

PROG

(Python)

def a(n, adict={0:0, 1:0, 2:0, 3:1, 4:3}):

.if n in adict:

..return adict[n]

.adict[n]=3*a(n-1) - a(n-2) - a(n-3) - a(n-4) - 2*a(n-5)

.return adict[n] # David Nacin, Mar 07 2012

(PARI) a(n)=([0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1; -2, -1, -1, -1, 3]^(n-1)*[0; 0; 0; 1; 3])[1, 1] \\ Charles R Greathouse IV, Feb 09 2017

CROSSREFS

Cf. A008466, A050231, A050233.

Sequence in context: A284943 A026712 A308370 * A050233 A143662 A151975

Adjacent sequences:  A050229 A050230 A050231 * A050233 A050234 A050235

KEYWORD

nonn,nice,easy

AUTHOR

Eric W. Weisstein

STATUS

approved

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Last modified October 1 17:45 EDT 2020. Contains 337444 sequences. (Running on oeis4.)