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A263342 Irregular triangle read by rows: T(n,k) is the number of unlabeled graphs with n vertices containing exactly k non-isomorphic induced subgraphs, 1 <= n <= k < A370001(n).

%I A263342 #19 Mar 10 2024 00:20:21
%S A263342 1,2,2,2,2,2,5,2,2,0,1,8,4,10,7,2,2,0,0,4,4,6,6,14,16,14,22,16,20,16,
%T A263342 10,4,2,2,0,0,0,0,4,4,4,10,8,8,16,10,20,32,42,36,40,48,74,56,68,76,60,
%U A263342 74,72,60,72,64,26,34,14,8,2
%N A263342 Irregular triangle read by rows: T(n,k) is the number of unlabeled graphs with n vertices containing exactly k non-isomorphic induced subgraphs, 1 <= n <= k < A370001(n).
%C A263342 Row sums give A000088, n >= 1.
%C A263342 There are at most A000171(n) odd terms in the n-th row, because complementary graphs have the same number of induced subgraphs. - _Pontus von Brömssen_, Mar 09 2024
%H A263342 Pontus von Brömssen, <a href="/A263342/b263342.txt">Table of n, a(n) for n = 1..279</a> (rows n = 1..9)
%H A263342 FindStat - Combinatorial Statistic Finder, <a href="http://www.findstat.org/StatisticsDatabase/St000087">The number of induced subgraphs</a>.
%F A263342 T(n,n) = 2 for n >= 2, because the empty graph and the complete graph are the only n-vertex graphs having only n non-isomorphic induced subgraphs. - _Pontus von Brömssen_, Mar 09 2024
%e A263342 Triangle begins:
%e A263342   1;
%e A263342   2;
%e A263342   2,2;
%e A263342   2,2,5,2;
%e A263342   2,0,1,8,4,10,7,2;
%e A263342   2,0,0,4,4,6,6,14,16,14,22,16,20,16,10,4,2;
%e A263342   ...
%Y A263342 Cf. A000088, A000171, A370001.
%K A263342 nonn,tabf
%O A263342 1,2
%A A263342 _Christian Stump_, Oct 15 2015
%E A263342 a(34) and beyond from _Pontus von Brömssen_, Mar 09 2024