A361410 -id:A361410 - 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.

A361407 Number of connected cubic graphs on 2n unlabeled vertices rooted at a vertex.

Original entry on oeis.org

0, 1, 2, 10, 64, 490, 4595, 51063, 657623, 9592204, 155630924, 2771922417, 53673859357, 1121581872170, 25143397213226, 601751140758134, 15310778492310274, 412656423154230159, 11743600063060974656, 351882591907696156959

Offset: 1

Andrew Howroyd, Mar 11 2023

nonn

Column k=1 of A321304.

Cf. A002851, A005638, A361408, A361410.

G.f.: B(x)/C(x) where B(x) is the g.f. of A361410 and C(x) is the g.f. of A005638.

A361411 Number of cubic graphs on 2n unlabeled vertices rooted at a pair of indistinguishable vertices.

Original entry on oeis.org

0, 1, 5, 33, 257, 2443, 27682, 363759, 5405697, 89134360, 1609418390, 31525697245, 665263778962, 15039817276939, 362579178545598, 9284375250749758, 251643492565059981, 7197256536139662143, 216621907269166632361, 6844093745422473471562

Offset: 1

Andrew Howroyd, Mar 11 2023

nonn

Column k=2 of A361361.

Cf. A005638, A361408, A361410.

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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A361407 Number of connected cubic graphs on 2n unlabeled vertices rooted at a vertex.

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A361411 Number of cubic graphs on 2n unlabeled vertices rooted at a pair of indistinguishable vertices.

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

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