

A269228


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


3



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
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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 BousquetMélou's paper cited below.
The first five terms are the same as in the sequence A005435.
A005435(n) is the number of columnconvex 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. BousquetMélou, A method for the enumeration of various classes of columnconvex polygons, Discrete Math. 154 (1996), 125.
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 A215973
Adjacent sequences: A269225 A269226 A269227 * A269229 A269230 A269231


KEYWORD

nonn


AUTHOR

Svjetlan Feretic, Jul 11 2016


STATUS

approved



