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Triangle read by rows: T(n,k) is the number of connected graphs on n unlabeled nodes with circumference k, (n >= 3, k >= 3).
4

%I #7 Sep 06 2019 21:49:02

%S 1,1,3,4,6,8,10,24,24,48,30,87,116,226,383,83,342,527,1283,2663,6196,

%T 257,1324,2644,6644,17613,55468,177083

%N Triangle read by rows: T(n,k) is the number of connected graphs on n unlabeled nodes with circumference k, (n >= 3, k >= 3).

%C Trees are excluded since they do not have any cycle.

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

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

%e Triangle begins:

%e 1;

%e 1, 3;

%e 4, 6, 8;

%e 10, 24, 24, 48;

%e 30, 87, 116, 226, 383;

%e 83, 342, 527, 1283, 2663, 6196;

%e 257, 1324, 2644, 6644, 17613, 55468, 177083;

%e ...

%Y Right diagonal is A003216.

%Y Row sums are A241841.

%Y Cf. A128042, A309524, A325447.

%K nonn,tabl,more

%O 3,3

%A _Andrew Howroyd_, Sep 06 2019