A390643 Triangle read by rows: T(n,k) = number of connected cubic graphs on 2n vertices with crossing number k for n >= 2, k >= 0.

0, 1, 1, 1, 3, 2, 9, 8, 2, 32, 40, 13, 133, 254, 114, 8, 681, 1858, 1347, 172, 2, 3893, 15236, 17241, 4753, 176, 2, 24809, 131576, 222231, 117307, 14308, 255, 3, 169206, 1170670, 2769288, 2444803, 713901, 51178, 397, 4

Offset

1,5

Links

Table of n, a(n) for n=1..42.

Eric Weisstein's World of Mathematics, Connected Graph.

Eric Weisstein's World of Mathematics, Cubic Graph.

Formula

T(n,0) = A005964(n).

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

Example

Triangle starts:
  0,
  1
  1,1
  3,2
  9,8,2
  32,40,13
  133,254,114,8
  681,1858,1347,172,2
  3893,15236,17241,4753,176,2
  24809,131576,222231,117307,14308,255,3
  169206,1170670,2769288,2444803,713901,51178,397,4

Crossrefs

Cf. A005964 (planar cubic connected graphs).

Cf. A002851 (cubic connected graphs).

Cf. A110507 (vertices in the smallest cubic graph with crossing number n).

Cf. A307450 (number of smallest cubic graph with crossing number n).

Cf. A390644 (triangle of crossing number tallies for quartic graphs).

Sequence in context: A124003 A159588 A321572 * A118045 A276023 A268822

Adjacent sequences: A390640 A390641 A390642 * A390644 A390645 A390646

Keyword

nonn,tabf,more

Author

Eric W. Weisstein, Nov 13 2025

Extensions

Row for n = 11 added by Eric W. Weisstein, Feb 03 2026

Status

approved