A352067 - OEIS

%I #18 Mar 07 2022 07:55:46

%S 1,0,1,0,1,1,0,2,3,1,0,3,13,4,1,0,6,62,37,6,1,0,11,364,393,77,7,1,0,

%T 23,2799,6485,1665,135,9,1,0,47,27811,158766,68957,5268,220,10,1,0,

%U 106,349306,5718805,5091421,541593,14997,330,12,1

%N Triangle read by rows: T(n,k) is the number of connected graphs with n nodes and degeneracy k, 0 <= k < n.

%H Pontus von Brömssen, <a href="/A352067/b352067.txt">Rows n = 1..11, flattened</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Degeneracy_(graph_theory)">Degeneracy</a>

%e Triangle begins:

%e   n\k| 0   1      2       3       4      5     6   7  8  9

%e   ---+----------------------------------------------------

%e    1 | 1

%e    2 | 0   1

%e    3 | 0   1      1

%e    4 | 0   2      3       1

%e    5 | 0   3     13       4       1

%e    6 | 0   6     62      37       6      1

%e    7 | 0  11    364     393      77      7     1

%e    8 | 0  23   2799    6485    1665    135     9   1

%e    9 | 0  47  27811  158766   68957   5268   220  10  1

%e   10 | 0 106 349306 5718805 5091421 541593 14997 330 12  1

%Y Row sums: A001349, column k=1: A000055.

%K nonn,tabl

%O 1,8

%A _Pontus von Brömssen_, Mar 05 2022