The On-Line Encyclopedia of Integer Sequences (OEIS)

A003125 revision #11

A003125

Value of an urn with n balls of type -1 and n+2 balls of type +1.
(Formerly M1929)

2, 9, 36, 142, 558, 2189, 8594, 33796, 133097, 524743, 2070466, 8177715, 32332378, 127948218, 506708043, 2007924808, 7960694208, 31576775077, 125313590701, 497543433995, 1976277486929, 7852859853208, 31214015140480, 124106224171554

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

REFERENCES

W. M. Boyce, On a simple optimal stopping problem, Discr. Math., 5 (1973), 297-312.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=1..24.

FORMULA

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).

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)}.

a(n) = B(n, n + 2). - Sean A. Irvine, Feb 02 2015

CROSSREFS

Sequence in context: A135593 A027995 A077836 * A055841 A037521 A037730

Adjacent sequences: A003122 A003123 A003124 * A003126 A003127 A003128

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Sean A. Irvine, Feb 02 2015

STATUS

editing