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 A232103 #31 Sep 24 2019 05:06:23 %S A232103 1,1,1,1,5,1,1,15,15,1,1,39,106,39,1,1,97,582,582,97,1,1,237,2952, %T A232103 6074,2952,237,1,1,575,14488,56778,56778,14488,575,1,1,1391,69982, %U A232103 510600,943340,510600,69982,1391,1,1,3361,335356,4502836,15009212,15009212 %N A232103 Square array read by antidiagonals: T(m,n) = number of ways of drawing a simple loop on an m x n rectangular lattice of dots in such a way that it touches each edge. %C A232103 This sequence is to be read as a table: %C A232103 1, 1, 1, 1, 1, ... %C A232103 1, 5, 15, 39, ... %C A232103 1, 15, 106, ... %C A232103 1, 39, ... %C A232103 1, ... %C A232103 ... %C A232103 This represents the number of simple, closed loops that can be formed on an m x n lattice of dots in such a way that it touches each edge. %C A232103 This sequence is related to A231829, called b(i,j) by a(i,j) = b(i,j) - 2 * b(i,j-1) + b(i,j-2) - 2 * b(i-1,j) + 4 * b(i-1,j-1) - 2 * b(j-1,j-2) + b(i-2,j) - 2 * b(i-2,j-1) + b(i-2,j-2). %C A232103 Equivalently, the number of fixed polyominoes without holes that have a width of m and height of n. - _Andrew Howroyd_, Oct 04 2017 %H A232103 Andrew Howroyd, <a href="/A232103/b232103.txt">Table of n, a(n) for n = 1..325</a> %H A232103 Jean-François Alcover, <a href="/A232103/a232103.txt">Mathematica program</a> %F A232103 T(m, n) = U(m, n) - 2*U(m, n-1) + U(m, n-2) where U(m, n) = V(m, n) - 2*V(m-1, n) + V(m-2, n) and V(m, n) = A231829(m, n). - _Andrew Howroyd_, Oct 04 2017 %e A232103 Array begins: %e A232103 ============================================================== %e A232103 m\n| 1 2 3 4 5 6 7 %e A232103 ---|---------------------------------------------------------- %e A232103 1 | 1 1 1 1 1 1 1... %e A232103 2 | 1 5 15 39 97 237 575... %e A232103 3 | 1 15 106 582 2952 14488 69982... %e A232103 4 | 1 39 582 6074 56778 510600 4502836... %e A232103 5 | 1 97 2952 56778 943340 15009212 234411981... %e A232103 6 | 1 237 14488 510600 15009212 419355340 11509163051... %e A232103 7 | 1 575 69982 4502836 234411981 11509163051 554485727288... %e A232103 ... - _Andrew Howroyd_, Oct 04 2017 %e A232103 a(3,2) is 15, thus: %e A232103 1) 2) 3) 4) 5) %e A232103 +-+-+-+ +-+-+-+ + +-+-+ +-+-+-+ +-+-+-+ %e A232103 | | | | | | | | | | %e A232103 + +-+-+ +-+ +-+ +-+ +-+ + + +-+ +-+-+ + %e A232103 | | | | | | | | | | %e A232103 +-+ + + + +-+ + +-+-+ + +-+-+ + + + +-+ %e A232103 6) 7) 8) 9) 10) %e A232103 +-+-+-+ +-+-+ + +-+-+-+ +-+ + + + +-+ + %e A232103 | | | | | | | | | | %e A232103 + +-+ + +-+ +-+ +-+ + + + +-+-+ +-+ +-+ %e A232103 | | | | | | | | | | | | %e A232103 +-+ +-+ + +-+-+ + +-+-+ +-+-+-+ +-+-+-+ %e A232103 11) 12) 13) 14) 15) %e A232103 +-+-+ + + + +-+ +-+ +-+ + +-+-+ +-+-+-+ %e A232103 | | | | | | | | | | | | %e A232103 + +-+ +-+-+ + + +-+ + +-+ + + + + + + %e A232103 | | | | | | | | | | %e A232103 +-+-+-+ +-+-+-+ +-+-+-+ +-+-+-+ +-+-+-+ %Y A232103 Rows 2-3 are A034182, A293263. %Y A232103 Main diagonal is A293261. %Y A232103 Cf. A231829, A292357. %K A232103 nonn,tabl %O A232103 1,5 %A A232103 _Douglas Boffey_, Nov 21 2013