A369279 - OEIS

%I #26 Mar 11 2024 23:12:54

%S 1,0,2,0,2,2,0,3,6,2,0,3,22,7,2,0,4,102,41,7,2,0,4,661,322,48,7,2,0,5,

%T 7606,4238,439,49,7,2,0,5,169021,98708,6396,480,49,7,2,0,6,7555003,

%U 4282954,159359,7301,487,49,7,2

%N Triangle read by rows: T(n,k) is the number of simple graphs on n unlabeled nodes with cooling number k = 1..n.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CoolingNumber.html">Cooling Number</a>.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SimpleGraph.html">Simple Graph</a>.

%e Triangle begins:

%e   1;

%e   0, 2;

%e   0, 2,       2;

%e   0, 3,       6,       2;

%e   0, 3,      22,       7,      2;

%e   0, 4,     102,      41,      7,    2;

%e   0, 4,     661,     322,     48,    7,   2;

%e   0, 5,    7606,    4238,    439,   49,   7,  2;

%e   0, 5,  169021,   98708,   6396,  480,  49,  7, 2;

%e   0, 6, 7555003, 4282954, 159359, 7301, 487, 49, 7, 2;

%e   ...

%Y Rows sums are A000088.

%Y Cf. A369280 (counts for connected graphs), A263322 (burning number).

%K nonn,tabl,more

%O 1,3

%A _Eric W. Weisstein_, Jan 18 2024