%I #9 Feb 27 2023 20:29:57
%S 0,1,1,3,8,3,6,25,25,6,10,58,94,58,10,15,117,270,270,117,15,21,218,
%T 681,1004,681,218,21,28,387,1597,3330,3330,1597,387,28,36,666,3592,
%U 10224,14864,10224,3592,666,36,45,1123,7880,29924,61165,61165,29924,7880,1123,45
%N Array read by antidiagonals: T(m,n) is the number of induced paths in the grid graph P_m X P_n.
%C Paths of length zero are not counted here.
%H Andrew Howroyd, <a href="/A360199/b360199.txt">Table of n, a(n) for n = 1..435</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GridGraph.html">Grid Graph</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Induced_path">Induced path</a>.
%e Array begins:
%e ============================================================
%e m\n| 1 2 3 4 5 6 7 8 ...
%e ---+--------------------------------------------------------
%e 1 | 0 1 3 6 10 15 21 28 ...
%e 2 | 1 8 25 58 117 218 387 666 ...
%e 3 | 3 25 94 270 681 1597 3592 7880 ...
%e 4 | 6 58 270 1004 3330 10224 29924 85036 ...
%e 5 | 10 117 681 3330 14864 61165 238897 907148 ...
%e 6 | 15 218 1597 10224 61165 334536 1723535 8647932 ...
%e 7 | 21 387 3592 29924 238897 1723535 11546874 75134416 ...
%e 8 | 28 666 7880 85036 907148 8647932 75134416 629381852 ...
%e ...
%Y Main diagonal is A360200.
%Y Rows 1..2 are A000217(n-1), A360201.
%Y Cf. A287151 (induced connected subgraphs), A288518 (undirected paths), A360196 (induced cycles), A360202 (induced trees), A360916 (maximum induced paths).
%K nonn,tabl
%O 1,4
%A _Andrew Howroyd_, Jan 29 2023