cp's OEIS Frontend

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

%I A269228 #41 Oct 23 2019 16:19:04
%S A269228 1,2,7,28,122,556,2618,12634,62128,310212,1568495,8014742,41323641,
%T A269228 214719610,1123244757,5910863420,31268459118,166185855552,
%U A269228 886961294034,4751819567488,25545030878475,137756210983218,745003421378887,4039670554117446,21957581725458521
%N A269228 Number of nondirected diagonally convex polyominoes with perimeter 2n + 2.
%C A269228 The generating function satisfies an algebraic equation of degree eight. I computed that generating function using the "turbo Temperley" method.
%C A269228 The formula for the generating function is given in the enclosed Maple worksheet.
%C A269228 The most practical version of the "turbo Temperley" method was given in Bousquet-Mélou's paper cited below.
%C A269228 The first five terms are the same as in the sequence A005435.
%C A269228 A005435(n) is the number of column-convex polyominoes with perimeter 2n + 2.
%C A269228 A049124(n) is the number of directed diagonally convex polyominoes with perimeter 2n.
%H A269228 Svjetlan Feretic, <a href="/A269228/b269228.txt">Table of n, a(n) for n = 1..100</a>
%H A269228 M. Bousquet-Mélou, <a href="http://dx.doi.org/10.1016/0012-365X(95)00003-F">A method for the enumeration of various classes of column-convex polygons</a>, Discrete Math. 154 (1996), 1-25.
%H A269228 Svjetlan Feretić, <a href="/A269228/a269228_3.mw.txt">Maple worksheet with g.f.</a>
%H A269228 Svjetlan Feretić, <a href="/A269228/a269228_4.mw.txt">the first one hundred terms of the sequence A269228</a>
%H A269228 Svjetlan Feretić, <a href="https://arxiv.org/abs/1907.09409">The perimeter generating function for nondirected diagonally convex polyominoes</a>, arXiv:1907.09409 [math.CO], 2019.
%e A269228 a(7) = 2618, so there are 2618 nondirected diagonally convex polyominoes with perimeter 2*7 + 2 = 16.
%Y A269228 Cf. A005435, A049124.
%K A269228 nonn
%O A269228 1,2
%A A269228 _Svjetlan Feretic_, Jul 11 2016