A269228 Number of nondirected diagonally convex polyominoes with perimeter 2n + 2.

1, 2, 7, 28, 122, 556, 2618, 12634, 62128, 310212, 1568495, 8014742, 41323641, 214719610, 1123244757, 5910863420, 31268459118, 166185855552, 886961294034, 4751819567488, 25545030878475, 137756210983218, 745003421378887, 4039670554117446, 21957581725458521

Offset

1,2

Comments

The generating function satisfies an algebraic equation of degree eight. I computed that generating function using the "turbo Temperley" method.

The formula for the generating function is given in the enclosed Maple worksheet.

The most practical version of the "turbo Temperley" method was given in Bousquet-Mélou's paper cited below.

The first five terms are the same as in the sequence A005435.

A005435(n) is the number of column-convex polyominoes with perimeter 2n + 2.

A049124(n) is the number of directed diagonally convex polyominoes with perimeter 2n.

Links

Svjetlan Feretic, Table of n, a(n) for n = 1..100

M. Bousquet-Mélou, A method for the enumeration of various classes of column-convex polygons, Discrete Math. 154 (1996), 1-25.

Svjetlan Feretić, Maple worksheet with g.f.

Svjetlan Feretić, the first one hundred terms of the sequence A269228

Svjetlan Feretić, The perimeter generating function for nondirected diagonally convex polyominoes, arXiv:1907.09409 [math.CO], 2019.

Example

a(7) = 2618, so there are 2618 nondirected diagonally convex polyominoes with perimeter 2*7 + 2 = 16.

Crossrefs

Cf. A005435, A049124.

Sequence in context: A150659 A150660 A150661 * A005435 A291091 A380681

Adjacent sequences: A269225 A269226 A269227 * A269229 A269230 A269231

Keyword

nonn

Author

Svjetlan Feretic, Jul 11 2016

Status

approved