A390623 Cluster series for percolation on the cells of the Cairo tiling.

1, 5, 14, 33, 76, 175, 360, 809, 1618, 3399, 7074, 13506, 29280, 54207

Offset

0,2

Comments

a(n) is the coefficient of p^(n+1) in the power series expansion of the expected finite size of the cluster containing a given cell for percolation with probability p. If the given cell is not open, its cluster is empty. Equivalently, a(n) can be taken to be the coefficient of p^n if we condition on the event that the given cell is open.

Links

Table of n, a(n) for n=0..13.

Wikipedia, Cairo pentagonal tiling.

Index entries for sequences related to cluster series.

Crossrefs

Cf. A003202, A003203, A003204, A196991, A219529, A383735, A390624.

Sequence in context: A038090 A094002 A188589 * A105082 A059821 A296010

Adjacent sequences: A390620 A390621 A390622 * A390624 A390625 A390626

Keyword

nonn,more

Author

Pontus von Brömssen, Nov 15 2025

Status

approved