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A215863 Number of simple labeled graphs on n+3 nodes with exactly n connected components that are trees or cycles. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 25 2012
STATUS
approved

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Last modified March 1 14:57 EST 2024. Contains 370433 sequences. (Running on oeis4.)