A046342 -id:A046342 - cp's OEIS frontend

A056711 Plug g.f. for A000108 (minus the leading 1), 1/2(1-(1-4x)^(1/2))/x - 1, into cycle index for dihedral group D_3.

0, 0, 0, 1, 2, 8, 28, 100, 358, 1309, 4772, 17556, 64782, 240090, 892662, 3329942, 12456782, 46725350, 175698056, 662193908, 2501118956, 9465771967, 35891640172, 136331485336, 518702002350, 1976588406300, 7543137149256, 28826327724850, 110304963059048

Offset: 0

N. J. A. Sloane, Jan 19 2001

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Cf. A000108, A058855, A046342.

Column k=3 of A275431.

Cycle index for D_3: 1/6*Z[1]^3+1/2*Z[1]*Z[2]+1/3*Z[3].

O.g.f.: 1/6*A(x)^3 + 1/2*A(x)*A(x^2) + 1/3*A(x^3), with A(x):=1/2*(1-(1-4*x)^(1/2))/x - 1 (see the name). For the cycle index of the dihedral group D_n see A212355 for the Harary-Palmer reference, the formula and a link. - Wolfdieter Lang, Jun 02 2012

A342770 T(n,k) is the number of rooted plane binary forests with n nodes and k trees: triangle read by rows.

Original entry on oeis.org

1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 0, 3, 0, 1, 0, 1, 0, 5, 0, 3, 0, 1, 0, 1, 0, 0, 7, 0, 3, 0, 1, 0, 1, 0, 14, 0, 8, 0, 3, 0, 1, 0, 1, 0, 0, 22, 0, 8, 0, 3, 0, 1, 0, 1, 0, 42, 0, 24, 0, 8, 0, 3, 0, 1, 0, 1, 0, 0, 66, 0, 25, 0, 8, 0

Offset: 0

R. J. Mathar, Mar 21 2021

Multiset transform of A126120.

			See A222006 showing T(6,k).
The triangle starts (n>=0, 0<=k<=n):
  1
  0   1
  0   0   1
  0   1   0   1
  0   0   1   0   1
  0   2   0   1   0   1
  0   0   3   0   1   0   1
  0   5   0   3   0   1   0   1
  0   0   7   0   3   0   1   0   1
  0  14   0   8   0   3   0   1   0   1
  0   0  22   0   8   0   3   0   1   0   1
  0  42   0  24   0   8   0   3   0   1   0   1
  0   0  66   0  25   0   8   0   3   0   1   0   1
  0 132   0  74   0  25   0   8   0   3   0   1   0   1
  0   0 217   0  76   0  25   0   8   0   3   0   1   0   1

Cf. A222006 (row sums), A126120 (column k=1), A007595 (k=2), A046342 (k=3), A088327 (limit n->oo, row reverse).

cp's OEIS Frontend

A056711 Plug g.f. for A000108 (minus the leading 1), 1/2(1-(1-4x)^(1/2))/x - 1, into cycle index for dihedral group D_3.

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Formula

A342770 T(n,k) is the number of rooted plane binary forests with n nodes and k trees: triangle read by rows.

Views

Author

Keywords

Comments

Examples

Crossrefs

cp's OEIS Frontend

A056711 Plug g.f. for A000108 (minus the leading 1), 1/2*(1-(1-4*x)^(1/2))/x - 1, into cycle index for dihedral group D_3.

Views

Author

Keywords

Links

Crossrefs

Formula

A342770 T(n,k) is the number of rooted plane binary forests with n nodes and k trees: triangle read by rows.

Views

Author

Keywords

Comments

Examples

Crossrefs

A056711 Plug g.f. for A000108 (minus the leading 1), 1/2(1-(1-4x)^(1/2))/x - 1, into cycle index for dihedral group D_3.