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A159061 Nearest integer to the expected number of tosses of a fair coin required to obtain at least n heads and n tails.

%I A159061 #17 Mar 05 2024 14:41:54
%S A159061 3,6,8,10,12,15,17,19,21,24,26,28,30,32,34,36,39,41,43,45,47,49,51,53,
%T A159061 56,58,60,62,64,66,68,70,72,75,77,79,81,83,85,87,89,91,93,95,98,100,
%U A159061 102,104,106,108,110,112,114,116,118,120,123,125,127,129,131,133,135,137
%N A159061 Nearest integer to the expected number of tosses of a fair coin required to obtain at least n heads and n tails.
%C A159061 For any n, either a(n+1)-a(n)=2 or a(n+1)-a(n)=3.
%D A159061 M. Griffiths, The Backbone of Pascal's Triangle, United Kingdom Mathematics Trust, 2008, pp. 68-72.
%H A159061 Martin Griffiths, <a href="https://www.jstor.org/stable/3621443">How many children?</a>, Math. Gaz., 90 (2006), 146-149.
%H A159061 Martin Griffiths and Alexander Bramham, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL16/Griffiths/griffiths22.html">Expectations of Family Sizes Subject to Minimum Numbers of Each Gender</a>, Journal of Integer Sequences, Vol. 16 (2013), #13.1.1.
%F A159061 a(n) is the nearest integer to 2*n*(1+ binomial(2*n,n)/(2^(2*n))).
%t A159061 a[n_] := Round[2 n (1 + Binomial[2 n, n]/(2^(2 n)))]; Array[a, 65] (* _Robert G. Wilson v_, Apr 05 2009 *)
%o A159061 (PARI) a(n) = round(2*n*(1+ binomial(2*n,n)/(2^(2*n)))) \\ _Felix Fröhlich_, Jan 23 2019
%Y A159061 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.
%K A159061 easy,nonn
%O A159061 1,1
%A A159061 _Martin Griffiths_, Apr 04 2009
%E A159061 More terms from _Robert G. Wilson v_, Apr 05 2009