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Search: id:A159062
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| A159062 |
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Nearest integer to the variance of the 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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| 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 16, 17, 18, 19, 20, 21, 22, 22, 23, 24, 25, 26, 27, 27, 28, 29, 30, 31, 32, 32, 33, 34, 35, 36, 37, 37, 38, 39, 40, 41, 41, 42, 43, 44, 45, 45, 46, 47, 48, 49, 49, 50, 51, 52, 53, 53, 54, 55, 56, 57, 57, 58, 59, 60, 61, 61, 62
(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)=0 or a(n+1)-a(n)=1.
a(n)/b(n) tends to 1 - 2/pi as n tends to infinity, where b(n) is the nth term of A159061.
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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)))-((n*binomial(2*n,n))/(2^(2*n-1)))^2
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MATHEMATICA
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f[n_] := Round[2^(1 - 4 n) n (16^n + Binomial[2 n, n] (4^n - 2 n Binomial[2 n, n]))]; Array[f, 72]
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CROSSREFS
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The nearest integer to the expected number of tosses of a fair coin required to obtain at least n heads and n tails is given in A159061.
Sequence in context: A117657 A106618 A080684 this_sequence A093616 A089247 A106620
Adjacent sequences: A159059 A159060 A159061 this_sequence A159063 A159064 A159065
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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
Formula clarified by the author, Apr 06 2009
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