A159061 Nearest integer to the expected number of tosses of a fair coin required to obtain at least n heads and n tails.
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
Offset: 1
References
- M. Griffiths, The Backbone of Pascal's Triangle, United Kingdom Mathematics Trust, 2008, pp. 68-72.
Links
- Martin Griffiths, How many children?, Math. Gaz., 90 (2006), 146-149.
- Martin Griffiths and Alexander Bramham, Expectations of Family Sizes Subject to Minimum Numbers of Each Gender, Journal of Integer Sequences, Vol. 16 (2013), #13.1.1.
Crossrefs
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.
Programs
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Mathematica
a[n_] := Round[2 n (1 + Binomial[2 n, n]/(2^(2 n)))]; Array[a, 65] (* Robert G. Wilson v, Apr 05 2009 *)
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PARI
a(n) = round(2*n*(1+ binomial(2*n,n)/(2^(2*n)))) \\ Felix Fröhlich, Jan 23 2019
Formula
a(n) is the nearest integer to 2*n*(1+ binomial(2*n,n)/(2^(2*n))).
Extensions
More terms from Robert G. Wilson v, Apr 05 2009
Comments