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 A287151 #14 Feb 16 2025 08:33:46 %S A287151 1,3,3,6,13,6,10,40,40,10,15,108,218,108,15,21,275,1126,1126,275,21, %T A287151 28,681,5726,11506,5726,681,28,36,1664,28992,116166,116166,28992,1664, %U A287151 36,45,4040,146642,1168586,2301877,1168586,146642,4040,45,55,9779,741556,11749134,45280509,45280509,11749134,741556,9779,55 %N A287151 Array read by antidiagonals: T(m,n) = number of nonzero m X n binary arrays with all 1's connected. %C A287151 Also the number of connected induced (non-null) subgraphs of the grid graph P_m X P_n. %C A287151 All rows (or columns) are linear recurrences with constant coefficients and the order of the recurrence of row m is at most 1 + A378941(m+1). At least for columns up to 7, this bound gives the actual order of the recurrence. The second differences of any column give those arrays that touch the top and bottom boundaries and have a recurrence order of 2 less since a finite state machine to enumerate these does not require states for empty rows. The number of states required is also considered in A140662 but does not take symmetry into account. - _Andrew Howroyd_, Dec 18 2024 %H A287151 Andrew Howroyd, <a href="/A287151/b287151.txt">Table of n, a(n) for n = 1..435</a> %H A287151 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ConnectedGraph.html">Connected Graph</a> %H A287151 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GridGraph.html">Grid Graph</a> %H A287151 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/InducedSubgraph.html">Induced Subgraph</a> %e A287151 Table starts: %e A287151 ==================================================================== %e A287151 m\n| 1 2 3 4 5 6 7 %e A287151 ---|---------------------------------------------------------------- %e A287151 1 | 1 3 6 10 15 21 28 ... %e A287151 2 | 3 13 40 108 275 681 1664 ... %e A287151 3 | 6 40 218 1126 5726 28992 146642 ... %e A287151 4 | 10 108 1126 11506 116166 1168586 11749134 ... %e A287151 5 | 15 275 5726 116166 2301877 45280509 889477656 ... %e A287151 6 | 21 681 28992 1168586 45280509 1732082741 66037462454 ... %e A287151 7 | 28 1664 146642 11749134 889477656 66037462454 4872949974666 ... %e A287151 ... %Y A287151 Rows 2..5 are A059020, A059021, A059524, A378940. %Y A287151 Main diagonal is A059525. %Y A287151 Cf. A116469, A140662, A286139, A286189, A292357, A378941. %K A287151 nonn,tabl %O A287151 1,2 %A A287151 _Andrew Howroyd_, May 20 2017