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 A320500 #24 Nov 13 2018 17:45:29 %S A320500 1,2,2,1,4,1,1,6,6,1,1,12,11,12,1,1,20,30,30,20,1,1,36,75,110,75,36,1, %T A320500 1,64,173,382,382,173,64,1,1,112,434,1270,1804,1270,434,112,1,1,200, %U A320500 1054,4298,7888,7888,4298,1054,200,1 %N A320500 Symmetric array read by antidiagonals: T(m,n) = number of "minimal connected vertex covers" of an m X n grid, for m>=1, n>=1. %C A320500 Take the m X n grid graph with m*n vertices, each connected to four neighbors [except only two at the corners, otherwise three on the edges]. We ask for a vertex cover that is connected. It should also be minimal: if we leave out any element and it is no longer a connected vertex cover. %H A320500 M. R. Garey and D. S. Johnson, <a href="https://www.jstor.org/stable/2100192">The rectilinear Steiner tree problem is NP-complete</a>, SIAM J. Applied Math., 32 (1977), 826-834. [They call these "connected node covers".] %e A320500 The array begins: %e A320500 1, 2, 1, 1, 1, 1, 1, 1, 1, ... %e A320500 2, 4, 6, 12, 20, 36, 64, 112, 200, ... %e A320500 1, 6, 11, 30, 75, 173, 434, 1054, 2558, ... %e A320500 1, 12, 30, 110, 382, 1270, 4298, 14560, 49204, ... %e A320500 1, 20, 75, 382, 1804, 7888, 36627, 166217, 755680, ... %e A320500 1, 36, 173, 1270, 7888, 46416, 287685, 1751154, 10656814, ... %e A320500 1, 64, 434, 4298, 36627, 287685, 2393422, 19366411, 157557218, ... %e A320500 1, 112, 1054, 14560, 166217, 1751154, 19366411, 208975042, 2255742067, ... %e A320500 1, 200, 2558, 49204, 755680, 10656814, 157557218, 2255742067, 32411910059, ... %e A320500 ... %e A320500 The T(3,3) = 11 minimal connected vertex covers of a 3 X 3 grid are: %e A320500 X.X .X. X.. X.X X.. X.. ..X ... ... .X. ... %e A320500 ... ... ..X ... ..X .X. .X. .X. .X. ... X.X %e A320500 X.X X.X X.. .X. X.. ... ... X.. ..X .X. ... %Y A320500 Row 2 appears to be (essentially) A107383 (or twice A061279). %Y A320500 The main diagonal is A320501. %Y A320500 Rows 3,4,5 are A320482, A320483, A320484. %K A320500 nonn,tabl %O A320500 1,2 %A A320500 _N. J. A. Sloane_, Oct 22 2018, based on email from _Don Knuth_, Oct 20 2018