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A050231
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a(n) is the number of n-tosses having a run of 3 or more heads for a fair coin (i.e. probability is a(n)/2^n).
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9
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0, 0, 1, 3, 8, 20, 47, 107, 238, 520, 1121, 2391, 5056, 10616, 22159, 46023, 95182, 196132, 402873, 825259, 1686408, 3438828, 6999071, 14221459, 28853662, 58462800, 118315137, 239186031, 483072832, 974791728, 1965486047
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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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.
Erich Friedman, Illustration of initial terms
Index to sequences with linear recurrences with constant coefficients, signature (3,-1,-1,-2).
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FORMULA
| a(n) = 2^n - Tribonacci(n+3), cf. A000073. - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 23 2003
G.f.:x^3/((1-2x)(1-x-x^2-x^3)) [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Jan 29 2009]
a(n) = 2 * a(n-1) + 2^(n-4) - a(n-4) since we can add T or H to a sequence of n-1 flips which has HHH, and H to one which ends in THH and does not have HHH among the first (n-4) flips [From Toby Gottfried Nov 20 2010].
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CROSSREFS
| Cf. A008466, A050232, A050233
Sequence in context: A138803 A048492 A006776 * A136305 A026712 A050232
Adjacent sequences: A050228 A050229 A050230 * A050232 A050233 A050234
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KEYWORD
| nonn,nice
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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