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A050232
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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).
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6
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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; internal format)
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OFFSET
| 1,5
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REFERENCES
| Feller, W. An Introduction to Probability Theory and Its Application, Vol. 1, 2nd ed. New York: Wiley, p. 300, 1968.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..300
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
| a(n) = 2^n - Tetranacci(n+4), cf. A000078. - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 23 2003
G.f.:x^4/((1-2x)(1-x-x^2-x^3-x^4)) [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Jan 29 2009]
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MATHEMATICA
| Flatten[With[{tetrnos=LinearRecurrence[{1, 1, 1, 1}, {0, 1, 1, 2}, 50]}, Table[ 2^n- Take[tetrnos, {n+3}], {n, 40}]]] (* From Harvey P. Dale, Dec 02 2011 *)
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CROSSREFS
| Cf. A008466, A050231, A050233
Sequence in context: A050231 A136305 A026712 * A050233 A143662 A001792
Adjacent sequences: A050229 A050230 A050231 * A050233 A050234 A050235
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KEYWORD
| nonn,nice
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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