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A050233
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a(n) is the number of n-tosses having a run of 5 or more heads for a fair coin (i.e. probability is a(n)/2^n).
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7
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0, 0, 0, 0, 1, 3, 8, 20, 48, 112, 255, 571, 1262, 2760, 5984, 12880, 27553, 58631, 124192, 262008, 550800, 1154256, 2412031, 5027575, 10455246, 21697060, 44940472, 92920992, 191818561, 395386763, 813872712, 1673157228
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OFFSET
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1,6
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COMMENTS
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a(n-1) is the number of compositions of n with at least one part >=6. [Joerg Arndt, Aug 06 2012]
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REFERENCES
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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
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T. D. Noe, Table of n, a(n) for n=1..300
Eric Weisstein's World of Mathematics, Run.
Index to sequences with linear recurrences with constant coefficients, signature (3,-1,-1,-1,-1,-2).
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FORMULA
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a(n) = 2^(n+1) - pentanacci(n+6), cf. A001591. - Vladeta Jovovic, Feb 23 2003
G.f.:x^5/((1-2*x)*(1-x-x^2-x^3-x^4-x^5)) [From Geoffrey Critzer, Jan 29 2009]
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MATHEMATICA
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f[x_] := x^4 / (1-3x+x^2+x^3+x^4+x^5+2x^6); CoefficientList[ Series[f[x], {x, 0, 31}], x] (* From Jean-François Alcover, Nov 18 2011 *)
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CROSSREFS
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Cf. A008466, A050231, A050232
Sequence in context: A136305 A026712 A050232 * A143662 A151975 A001792
Adjacent sequences: A050230 A050231 A050232 * A050234 A050235 A050236
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KEYWORD
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nonn,nice,changed
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AUTHOR
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Eric W. Weisstein
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STATUS
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approved
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