cp's OEIS Frontend

A331878 Number of (non-null) connected induced subgraphs in a right-triangular graph with n vertices on each side.

%I A331878 #27 Feb 16 2025 08:33:59
%S A331878 1,6,32,242,3389,94204,5152184,550554052,114558123057,46273463018266,
%T A331878 36187365370984792,54676438562307219806,159361336209506075254061,
%U A331878 894922393831489478287443136,9673844907264825614989071514624,201139020197000279384599867300494336
%N A331878 Number of (non-null) connected induced subgraphs in a right-triangular graph with n vertices on each side.
%C A331878 a(n) is the number of lower triangular n X n binary arrays with all 1's connected.
%C A331878 a(n) is the number of ways to place a fixed polyomino on an n X n grid with all squares above the main diagonal unoccupied.
%H A331878 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/InducedSubgraph.html">Induced Subgraph</a>
%H A331878 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Polyomino.html">Polyomino</a>
%e A331878 The graphs for n = 2 and n = 3 are illustrated below:
%e A331878                    o
%e A331878         o          |
%e A331878         |          o---o
%e A331878         o---o      |   |
%e A331878                    o---o---o
%e A331878 .
%e A331878 The a(2) = 6 connected induced subgraphs are:
%e A331878      X     o     o     X     o     X
%e A331878      o o   X o   o X   X o   X X   X X
%Y A331878 Cf. A059525, A268758, A287689.
%K A331878 nonn
%O A331878 1,2
%A A331878 _Andrew Howroyd_, May 03 2020