A391388 Site percolation series for square lattice: coefficients of the power series expansion in powers of q=1-p of the probability that a given site (not assumed to be open) belongs to the infinite cluster, where p is the probability that a site is open.

1, -1, 0, 0, -1, 1, -4, -4, -15, -5, -158, 234, -1349, 2713, -13704, 42676, -172825, 559053, -2029776, 6774936, -23900386, 81129962, -282099620, 963894132, -3331512669, 11422580633, -39350336472, 134939821080, -463383554563, 1586767676943, -5434335886108

Offset

0,7

Links

Table of n, a(n) for n=0..30.

A. R. Conway and A. J. Guttmann, On two-dimensional percolation, Journal of Physics A: Mathematical and General 28 (1995), 891-904. See Table 4.

Formula

a(n) = -Sum_{m>=1,k=max(0,n-m)..min(n,2*m+2)} A338210(m,k)*m*(-1)^(n-k)*binomial(m,n-k) for n >= 2.

a(n) = A391389(n)-A391389(n-1) for n >= 1.

Crossrefs

Cf. A338210, A391389, A391390, A391392.

Sequence in context: A174406 A270844 A287286 * A271546 A325655 A117187

Adjacent sequences: A391385 A391386 A391387 * A391389 A391390 A391391

Keyword

sign

Author

Pontus von Brömssen, Dec 10 2025

Extensions

a(17)-a(30) from the Conway-Guttmann paper added by Pontus von Brömssen, Dec 18 2025

Status

approved