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User: Svjetlan Feretic

Svjetlan Feretic has authored 1 sequences.

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

Svjetlan Feretic, Jul 11 2016

nonn

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.

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

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.

Cf. A005435, A049124.

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User: Svjetlan Feretic

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

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