A361361 Triangle read by rows: T(n,k) is the number of bicolored cubic graphs on 2n unlabeled vertices with k vertices of the first color, n >= 0, 0 <= k <= 2*n.

1, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 5, 5, 5, 2, 2, 6, 11, 33, 48, 66, 48, 33, 11, 6, 21, 68, 257, 556, 950, 1071, 950, 556, 257, 68, 21, 94, 510, 2443, 7126, 15393, 23644, 27606, 23644, 15393, 7126, 2443, 510, 94, 540, 4712, 27682, 102122, 270957, 526783, 781292, 887305, 781292, 526783, 270957, 102122, 27682, 4712, 540

Offset: 0

Author

Andrew Howroyd, Mar 10 2023

Keywords

• nonn
• tabf

Comments

Adjacent vertices may have the same color.

Examples

			Triangle begins:
  1
  0,   0,  0;
  1,   1,  1,    1,   1;
  2,   2,  5,    5,   5,    2,   2;
  6,  11, 33,   48,  66,   48,  33,  11,   6;
  21, 68, 257, 556, 950, 1071, 950, 556, 257, 68, 21;
  ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..440 (rows 0..20)

Crossrefs

Columns k=0..2 are A005638, A361410, A361411.

Row sums are A361362.

Central coefficients are A361409.

Cf. A321304 (connected), A361404.