A365949 - OEIS

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A365949

Irregular triangle read by rows: T(n,k) (0 <= k <= n^2) are coefficients of exact wrapping probability for site percolation on an n X n 2D square lattice with periodic boundary conditions. This is for the probability that it wraps in both dimensions.

0, 1, 0, 0, 0, 4, 1, 0, 0, 0, 0, 0, 9, 42, 36, 9, 1, 0, 0, 0, 0, 0, 0, 0, 16, 328, 1504, 2960, 2992, 1668, 560, 120, 16, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 25, 1510, 16300, 86925, 285200, 625550, 947740, 1004400, 754775, 412250, 168450, 52620, 12650, 2300, 300, 25, 1

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OFFSET

1,6

COMMENTS

The wrapping probability function is Sum_{k=0..n^2} T(n,k)*p^k*(1-p)^(n^2-k).

LINKS

Table of n, a(n) for n=1..60.

Stephan Mertens, Percolation (Gives first 7 rows)

EXAMPLE

Triangle begins:

0, 1,

0, 0, 0, 4, 1,