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A325455 Triangle read by rows: T(n,k) is the number of simple connected graphs on n unlabeled nodes with circumference k, (n >= 3, k >= 3).

%I A325455 #11 Feb 16 2025 08:33:58
%S A325455 1,1,3,4,6,8,10,24,24,48,30,87,116,226,383,83,342,527,1283,2663,6196,
%T A325455 257,1324,2644,6644,17613,55468,177083
%N A325455 Triangle read by rows: T(n,k) is the number of simple connected graphs on n unlabeled nodes with circumference k, (n >= 3, k >= 3).
%C A325455 Trees are excluded since they do not have any cycle.
%H A325455 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphCircumference.html">Graph Circumference</a>
%H A325455 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HamiltonianGraph.html">Hamiltonian Graph</a>
%e A325455 Triangle begins:
%e A325455     1;
%e A325455     1,    3;
%e A325455     4,    6,    8;
%e A325455    10,   24,   24,   48;
%e A325455    30,   87,  116,  226,   383;
%e A325455    83,  342,  527, 1283,  2663,  6196;
%e A325455   257, 1324, 2644, 6644, 17613, 55468, 177083;
%e A325455   ...
%Y A325455 Right diagonal is A003216.
%Y A325455 Row sums are A241841.
%Y A325455 Cf. A128042, A309524, A325447.
%K A325455 nonn,tabl,more
%O A325455 3,3
%A A325455 _Andrew Howroyd_, Sep 06 2019