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 A360199 #10 Feb 16 2025 08:34:04 %S A360199 0,1,1,3,8,3,6,25,25,6,10,58,94,58,10,15,117,270,270,117,15,21,218, %T A360199 681,1004,681,218,21,28,387,1597,3330,3330,1597,387,28,36,666,3592, %U A360199 10224,14864,10224,3592,666,36,45,1123,7880,29924,61165,61165,29924,7880,1123,45 %N A360199 Array read by antidiagonals: T(m,n) is the number of induced paths in the grid graph P_m X P_n. %C A360199 Paths of length zero are not counted here. %H A360199 Andrew Howroyd, <a href="/A360199/b360199.txt">Table of n, a(n) for n = 1..435</a> %H A360199 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GridGraph.html">Grid Graph</a>. %H A360199 Wikipedia, <a href="https://en.wikipedia.org/wiki/Induced_path">Induced path</a>. %e A360199 Array begins: %e A360199 ============================================================ %e A360199 m\n| 1 2 3 4 5 6 7 8 ... %e A360199 ---+-------------------------------------------------------- %e A360199 1 | 0 1 3 6 10 15 21 28 ... %e A360199 2 | 1 8 25 58 117 218 387 666 ... %e A360199 3 | 3 25 94 270 681 1597 3592 7880 ... %e A360199 4 | 6 58 270 1004 3330 10224 29924 85036 ... %e A360199 5 | 10 117 681 3330 14864 61165 238897 907148 ... %e A360199 6 | 15 218 1597 10224 61165 334536 1723535 8647932 ... %e A360199 7 | 21 387 3592 29924 238897 1723535 11546874 75134416 ... %e A360199 8 | 28 666 7880 85036 907148 8647932 75134416 629381852 ... %e A360199 ... %Y A360199 Main diagonal is A360200. %Y A360199 Rows 1..2 are A000217(n-1), A360201. %Y A360199 Cf. A287151 (induced connected subgraphs), A288518 (undirected paths), A360196 (induced cycles), A360202 (induced trees), A360916 (maximum induced paths). %K A360199 nonn,tabl %O A360199 1,4 %A A360199 _Andrew Howroyd_, Jan 29 2023