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

1,1

Comments

For any n, either a(n+1)-a(n)=2 or a(n+1)-a(n)=3.

References

M. Griffiths, The Backbone of Pascal's Triangle, United Kingdom Mathematics Trust, 2008, pp. 68-72.

Links

Table of n, a(n) for n=1..64.

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.

Formula

a(n) is the nearest integer to 2*n*(1+ binomial(2*n,n)/(2^(2*n))).

Mathematica

a[n_] := Round[2 n (1 + Binomial[2 n, n]/(2^(2 n)))]; Array[a, 65] (* Robert G. Wilson v, Apr 05 2009 *)

Prog

(PARI) a(n) = round(2*n*(1+ binomial(2*n, n)/(2^(2*n)))) \\ Felix Fröhlich, Jan 23 2019

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.

Sequence in context: A189467 A023983 A190058 * A257874 A180398 A128420

Adjacent sequences: A159058 A159059 A159060 * A159062 A159063 A159064

Keyword

easy,nonn

Author

Martin Griffiths, Apr 04 2009

Extensions

More terms from Robert G. Wilson v, Apr 05 2009

Status

approved