Journal of Integer Sequences, Vol. 16 (2013), Article 13.1.1

Expectations of Family Sizes Subject to Minimum Numbers of Each Gender

Martin Griffiths
Mathematical Institute
University of Oxford
Oxford OX1 3LB
United Kingdom

Alexander Bramham
Wadham College
University of Oxford
Oxford OX1 3PN
United Kingdom


We consider the infinite families of sequences that arise from a scenario involving the expected number of children born to a married couple when certain conditions are placed on the minimum number of each gender. We obtain both exact and asymptotic formulas for these expectations, and go on to consider the long-term behavior of sequences derived from them. For the situations studied here, it is shown that the long-term behavior of each of the resulting sequences always falls into one of two distinct categories.

Full version:  pdf,    dvi,    ps,    latex    

(Concerned with sequence A159061.)

Received December 14 2012; revised version received January 1 2013. Published in Journal of Integer Sequences, January 1 2013.

Return to Journal of Integer Sequences home page