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%I M1929 #18 Feb 03 2015 09:00:44
%S 2,9,36,142,558,2189,8594,33796,133097,524743,2070466,8177715,
%T 32332378,127948218,506708043,2007924808,7960694208,31576775077,
%U 125313590701,497543433995,1976277486929,7852859853208,31214015140480,124106224171554
%N Value of an urn with n balls of type -1 and n+2 balls of type +1.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H W. M. Boyce, <a href="http://dx.doi.org/10.1016/0012-365X(73)90123-4">On a simple optimal stopping problem</a>, Discr. Math., 5 (1973), 297-312.
%F A(m, p) = 0 for m < 0 or p < 0. A(0, 0) = 0. A(1, 0) = -1. A(0, 1) = 1. Otherwise, A(m, p) = A(m - 1, p) + A(m, p - 1).
%F B(m, p) = 0 for m < 0 or p < 0. Otherwise, B(m, p) = max{0, A(m, p) + B(m - 1, p) + B(m, p - 1)}.
%F a(n) = B(n, n + 2). - _Sean A. Irvine_, Feb 02 2015
%K nonn
%O 1,1
%A _N. J. A. Sloane_
%E More terms and title clarified by _Sean A. Irvine_, Feb 02 2015
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