A361404 -id:A361404 - cp's OEIS frontend

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

Andrew Howroyd, Mar 10 2023

Adjacent vertices may have the same color.

			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;
  ...

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

Columns k=0..2 are A005638, A361410, A361411.
Row sums are A361362.
Central coefficients are A361409.
Cf. A321304 (connected), A361404.

A361405 Number of graphs with loops on 2n unlabeled vertices with n loops.

Original entry on oeis.org

1, 2, 28, 1408, 580656, 2658827456, 146702084635392, 98485306566812364032, 820443196111261227164076544, 86804253216450161933010414314819072, 119212631345634236227720012129209606659383296, 2166023316743980619769969171366251471253351621687457792

Offset: 0

Andrew Howroyd, Mar 11 2023

nonn

a(n) is the number of bicolored graphs on 2n unlabeled nodes with an equal number of each color. Adjacent vertices may have the same color.

Andrew Howroyd, Table of n, a(n) for n = 0..25

Central coefficients of A361404.

Cf. A007139.

a(n) = row(2*n)[n+1] \\ row(n) defined in A361404.

a(n) = A361404(2*n, n).

cp's OEIS Frontend

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.

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