A128042 -id:A128042 - cp's OEIS frontend

A128242 Number of n-node (unlabeled) connected graphs with girth 5.

0, 0, 1, 1, 5, 16, 66, 266, 1235, 6350, 37364, 251106, 1942085, 17287710, 177086792, 2084120446, 28125888087, 434318629496, 7657513894860

Offset: 3

Keith Briggs, May 05 2007

Cf. A128041, A128042.

Cf. A128236, A128237, A128238, A128239, A128240, A128241, A128243.

geng -ctfq $n | countg -qg5 --ng # Martin Fuller, May 03 2015

Corrected and extended by Martin Fuller, May 01 2015

a(18)-a(21) added by Georg Grasegger, May 02 2023

A325447 Triangle read by rows: T(n,k) is the number of simple nonseparable (or 2-connected) graphs on n unlabeled nodes with circumference k, (n >= 3, k >= 3).

Original entry on oeis.org

1, 0, 3, 0, 2, 8, 0, 2, 6, 48, 0, 2, 9, 74, 383, 0, 2, 10, 159, 756, 6196, 0, 2, 13, 276, 2058, 14634, 177083, 0, 2, 14, 505, 4824, 48137, 384942, 9305118

Offset: 3

Andrew Howroyd, Sep 06 2019

			Triangle begins, (n >= 3, k >= 3):
  1;
  0, 3;
  0, 2,  8;
  0, 2,  6,  48;
  0, 2,  9,  74,  383;
  0, 2, 10, 159,  756,  6196;
  0, 2, 13, 276, 2058, 14634, 177083;
  0, 2, 14, 505, 4824, 48137, 384942, 9305118;
  ...

Eric Weisstein's World of Mathematics, Graph Circumference
Eric Weisstein's World of Mathematics, Hamiltonian Graph

Row sums are A002218(n >= 3).
Right diagonal is A003216.
Cf. A128042, A325455.

T(n, 4) = 2 for n > 4.

cp's OEIS Frontend

A128242 Number of n-node (unlabeled) connected graphs with girth 5.

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A325447 Triangle read by rows: T(n,k) is the number of simple nonseparable (or 2-connected) graphs on n unlabeled nodes with circumference k, (n >= 3, k >= 3).

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