A263342 - OEIS

%I #19 Mar 10 2024 00:20:21

%S 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 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 74,72,60,72,64,26,34,14,8,2

%N 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 Row sums give A000088, n >= 1.

%C 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 Pontus von Brömssen, <a href="/A263342/b263342.txt">Table of n, a(n) for n = 1..279</a> (rows n = 1..9)

%H FindStat - Combinatorial Statistic Finder, <a href="http://www.findstat.org/StatisticsDatabase/St000087">The number of induced subgraphs</a>.

%F 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 Triangle begins:

%e   1;

%e   2;

%e   2,2;

%e   2,2,5,2;

%e   2,0,1,8,4,10,7,2;

%e   2,0,0,4,4,6,6,14,16,14,22,16,20,16,10,4,2;

%e   ...

%Y Cf. A000088, A000171, A370001.

%K nonn,tabf

%O 1,2

%A _Christian Stump_, Oct 15 2015

%E a(34) and beyond from _Pontus von Brömssen_, Mar 09 2024