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Search: id:A159061
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| A159061 |
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Nearest integer to the expected number of tosses of a fair coin required to obtain at least n heads and n tails. |
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+0
2
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| 3, 6, 8, 10, 12, 15, 17, 19, 21, 24, 26, 28, 30, 32, 34, 36, 39, 41, 43, 45, 47, 49, 51, 53, 56, 58, 60, 62, 64, 66, 68, 70, 72, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 123, 125, 127, 129, 131, 133, 135, 137
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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For any n, either a(n+1)-a(n)=2 or a(n+1)-a(n)=3.
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REFERENCES
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M. Griffiths, How many children?, Math. Gaz., 90 (2006), 146-149.
M. Griffiths, The Backbone of Pascal's Triangle, United Kingdom Mathematics Trust, 2008, pp. 68-72.
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FORMULA
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a(n) is the nearest integer to 2*n*(1+ binomial(2*n,n)/(2^(2*n))).
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MATHEMATICA
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f[n_] := Round[2 n (1 + Binomial[2 n, n]/(2^(2 n)))]; Array[f, 65] - Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 05 2009
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CROSSREFS
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The nearest integer to the variance of the number of tosses of a fair coin required to obtain at least n heads and n tails is given in A159062.
Sequence in context: A108769 A112234 A023983 this_sequence A128420 A099135 A047282
Adjacent sequences: A159058 A159059 A159060 this_sequence A159062 A159063 A159064
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KEYWORD
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easy,nonn
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AUTHOR
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Martin Griffiths (griffm(AT)essex.ac.uk), Apr 04 2009
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 05 2009
More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 05 2009
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