login
A365957
Irregular triangle read by rows: T(N,k) (0 <= k <= 4*N^2) are coefficients of exact wrapping probability for site percolation on a 2*N X 2*N 2D hexagonal lattice with periodic boundary conditions. This is for the probability that it wraps in either dimension.
14
0, 0, 4, 4, 1, 0, 0, 0, 0, 4, 48, 272, 944, 2214, 3696, 4408, 3536, 1768, 560, 120, 16, 1, 0, 0, 0, 0, 0, 0, 462, 12456, 162810, 1370172, 8316297, 38643624, 142444695, 426043278, 1049742000, 2153912760, 3711426624, 5409742482, 6716638430, 7153883766, 6584406876, 5274811392, 3701882250, 2287146006, 1247224353, 600206400, 254134359, 94140796, 30260304, 8347680, 1947792, 376992, 58905, 7140, 630, 36, 1
OFFSET
1,3
COMMENTS
The wrapping probability function is Sum_{k=0..4*N^2} T(N,k)*p^k*(1-p)^(4*N^2-k).
EXAMPLE
Triangle begins:
0, 0, 4, 4, 1,
0, 0, 0, 0, 4, 48, 272, 944, 2214, 3696, 4408, 3536, 1768, 560, 120, 16, 1,
0, 0, 0, 0, 0, 0, 462, 12456, 162810, 1370172, 8316297, 38643624, 142444695, 426043278, 1049742000, 2153912760, 3711426624, 5409742482, 6716638430, 7153883766, 6584406876, 5274811392, 3701882250, 2287146006, 1247224353, 600206400, 254134359, 94140796, 30260304, 8347680, 1947792, 376992, 58905, 7140, 630, 36, 1,
...
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, Oct 12 2023
EXTENSIONS
The DATA shows three rows of the triangle.
STATUS
approved