This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A227004 #9 Jul 04 2013 03:52:53
%S A227004 1,1,1,1,1,0,0,1,1,3,4,2,2,0,0,0,0,1,1,3,13,20,17,6,10,5,0,1,0,0,0,0,
%T A227004 0,0,1,1,6,37,138,280,300,255,218,98,43,55,28,20,11,1,0,2,0,0,0,0,0,0,
%U A227004 0,0,1
%N A227004 Irregular triangle read by rows: T(n,k) is the number of inequivalent tilings by squares of an n X n square lattice that contain k nodes unconnected to any of their neighbors.
%C A227004 The n-th row contains (n-1)^2 + 1 elements.
%C A227004 The irregular triangle is shown below.
%C A227004 \ k 0 1 2 3 4 5 6 7 8 9 ...
%C A227004 n
%C A227004 1 1
%C A227004 2 1 1
%C A227004 3 1 1 0 0 1
%C A227004 4 1 3 4 2 2 0 0 0 0 1
%C A227004 5 1 3 13 20 17 6 10 5 0 1 ...
%C A227004 6 1 6 37 138 280 300 255 218 98 43 ...
%C A227004 7 1 6 75 505 2160 5410 8508 9179 8805 7917 ...
%H A227004 Christopher Hunt Gribble, <a href="/A227004/b227004.txt">Table of n, a(n) for n = 1..98</a>
%H A227004 Christopher Hunt Gribble, <a href="/A226978/a226978.txt">C++ program for A226978, A226979, A226980, A226981, A227004</a>
%F A227004 Sum_{k=0..(n-1)^2} T(n,k) = A224239(n).
%e A227004 For n = 4, there are 3 inequivalent tilings that contain 1 isolated node, so T(4,1) = 3.
%e A227004 A 2 X 2 square contains 1 isolated node.
%e A227004 Consider that each tiling is composed of ones and zeros where a one represents a node with one or more links to its neighbors and a zero represents a node with no links to its neighbors. Then the 3 tilings are:
%e A227004 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
%e A227004 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1
%e A227004 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1
%e A227004 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
%e A227004 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
%Y A227004 Cf. A224239.
%K A227004 nonn,tabf
%O A227004 1,10
%A A227004 _Christopher Hunt Gribble_, Jun 26 2013