A215863 Number of simple labeled graphs on n+3 nodes with exactly n connected components that are trees or cycles.

0, 19, 135, 540, 1610, 3990, 8694, 17220, 31680, 54945, 90805, 144144, 221130, 329420, 478380, 679320, 945744, 1293615, 1741635, 2311540, 3028410, 3920994, 5022050, 6368700, 8002800, 9971325, 12326769, 15127560, 18438490, 22331160, 26884440, 32184944, 38327520

Offset

0,2

Links

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

Formula

G.f.: (6*x^2-2*x-19)*x/(x-1)^7.

a(n) = C(n+3,4)*(n^2+13*n+24)/2.

Example

a(1) = 19:
.1-2.  .1-2.  .1 2.  .1-2.  .1-2.  .1 2.  .1 2.  .1 2.  .1-2.  .1-2.
.| |.  . X .  .|X|.  .|\ .  . /|.  . \|.  .|/ .  .| |.  .|  .  .| |.
.4-3.  .4-3.  .4.3.  .4.3.  .4.3.  .4-3.  .4-3.  .4-3.  .4-3.  .4.3.
.
.1-2.  .1 2.  .1-2.  .1-2.  .1-2.  .1 2.  .1 2.  .1 2.  .1 2.
.  |.  . X .  . / .  . \ .  . X .  .|/|.  . X|.  .|X .  .|\|.
.4-3.  .4-3.  .4-3.  .4-3.  .4.3.  .4.3.  .4.3.  .4.3.  .4.3.

Maple

a:= n-> binomial(n+3, 4)*(24+(13+n)*n)/2:
seq(a(n), n=0..40);

Crossrefs

A diagonal of A215861.

Sequence in context: A041692 A078977 A085464 * A101090 A213122 A211092

Adjacent sequences: A215860 A215861 A215862 * A215864 A215865 A215866

Keyword

nonn

Author

Alois P. Heinz, Aug 25 2012

Status

approved