A390644 Triangle read by rows: T(n,k) = number of connected quartic graphs on n vertices with crossing number k for n >= 1, k >= 0.

0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 2, 2, 0, 1, 1, 4, 6, 5, 3, 9, 28, 15, 3, 1, 3, 30, 97, 97, 31, 7, 13, 84, 411, 608, 349, 64, 14, 0, 1, 21, 285, 1635, 3795, 3508, 1284, 216, 32, 2, 68, 937, 6935, 21632, 31271, 20206, 6158, 888, 69, 3, 1, 166, 3343, 28497, 116203, 237068, 246345, 132339, 36654, 4579, 287, 10

Offset

1,12

Links

Eric W. Weisstein, Rows 1-16

Eric Weisstein's World of Mathematics, Connected Graph.

Eric Weisstein's World of Mathematics, Quartic Graph.

Formula

T(n,0) = A072552(n).

Sum_{k=0..kmax} T(n,k) = A002851(n).

Example

Triangle begins:
  0
  0
  0
  0
  0,1
  1
  0,1,1
  1,2,2,0,1
  1,4,6,5
  3,9,28,15,3,1
  3,30,97,97,31,7
  13,84,411,608,349,64,14,0,1
  21,285,1635,3795,3508,1284,216,32,2
  68,937,6935,21632,31271,20206,6158,888,69,3,1
  166,3343,28497,116203,237068,246345,132339,36654,4579,287,10
  543,11837,118604,590703,1593075,2389237,2037575,993453,264359,35577,2322,123,9,0,1

Crossrefs

Cf. A072552 (planar quartic connected graphs).

Cf. A002851 (cubic quartic graphs).

Cf. A389263 (vertices in the smallest quartic graph with crossing number n).

Cf. A389263 (number of smallest quartic graphs with crossing number n).

Cf. A390643 (triangle of crossing number tallies for cubic graphs).

Sequence in context: A264909 A378112 A104579 * A079531 A182882 A134178

Adjacent sequences: A390641 A390642 A390643 * A390645 A390646 A390647

Keyword

nonn,tabf,more

Author

Eric W. Weisstein, Nov 13 2025

Extensions

Row 15 from Eric W. Weisstein, Nov 21 2025

Status

approved