A361411 -id:A361411 - 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.

A361408 Number of connected cubic graphs on 2n unlabeled vertices rooted at a pair of indistinguishable vertices.

Original entry on oeis.org

0, 1, 5, 31, 248, 2382, 27233, 359800, 5364193, 88622485, 1602171855, 31410476113, 663240471075, 15001046054183, 361775504849332, 9266474332849318, 251217335356943672, 7186461542458525108, 216332059500870350414, 6835872042063656823802

Offset: 1

Andrew Howroyd, Mar 11 2023

nonn

Column k=2 of A321304.

Cf. A002851, A005638, A361407, A361411.

G.f.: B(x)/C(x) - (D(x) + D(x^2))/2 where B(x), C(x) and D(x) are the g.f.s of A361411, A005638 and A361407, respectively.

A361410 Number of cubic graphs on 2n unlabeled vertices rooted at a vertex.

Original entry on oeis.org

0, 1, 2, 11, 68, 510, 4712, 51877, 664520, 9662968, 156490473, 2783955994, 53863486240, 1124886942314, 25206326633070, 603048386506505, 15339533779133582, 413338072569232815, 11760801736217845686, 352342902996056683824

Offset: 1

Andrew Howroyd, Mar 11 2023

nonn

Column k=1 of A361361.

Cf. A005638, A361407, A361411.

A361409 Number of bicolored cubic graphs on 2n unlabeled vertices with n vertices of each color.

Original entry on oeis.org

1, 0, 1, 5, 66, 1071, 27606, 887305, 34583357, 1562797351, 80177945542, 4597212665432, 291214532031215, 20193430937073303, 1521240318892230748, 123711268485285686123, 10801367759750192440520, 1007762402877770768660697, 100058924666668698411972015, 10533938778032068908299390227, 1172080056205294525370971027435

Offset: 0

Andrew Howroyd, Mar 11 2023

nonn

Adjacent vertices may have the same color.

Central coefficients of A361361.

Cf. A005638, A361406, A361410, A361411.

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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A361408 Number of connected cubic graphs on 2n unlabeled vertices rooted at a pair of indistinguishable vertices.

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A361410 Number of cubic graphs on 2n unlabeled vertices rooted at a vertex.

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A361409 Number of bicolored cubic graphs on 2n unlabeled vertices with n vertices of each color.

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