

A366998


a(n) is the numerator of the maximum expected number of steps of a random walk on the square lattice until it lands on a mined lattice point, given that mines are placed on all but n points.


4



0, 1, 4, 12, 28, 8, 124, 128, 263, 9, 1303, 519707, 380, 3435
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OFFSET

0,3


COMMENTS

For all n <= 13 except n = 3, the optimal placement of the minefree points is unique, up to rotations and reflections with respect to the starting point. See linked illustration.


LINKS



EXAMPLE

For n = 0, the random walk stops before it can take any step, so a(0) = 0.
For n = 1, only the mine at the starting point can be swept, so the random walk always stops after 1 step and a(1) = 1.
For n = 2, the starting point and one adjacent point can be swept. The random walk then has probability 1/4 of surviving at each step, which implies that the expected number of steps is 4/3, so a(2) = 4. (The number of steps follows a geometric distribution.)


CROSSREFS



KEYWORD

nonn,frac,more


AUTHOR



STATUS

approved



