cp's OEIS Frontend

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.

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.

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%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