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A215983 Number of simple unlabeled graphs on n nodes with exactly 3 connected components that are trees or cycles. 3
1, 1, 3, 6, 12, 23, 47, 92, 189, 401, 869, 1949, 4475, 10520, 25183, 61366, 151555, 379164, 958555, 2446746, 6296819, 16326996, 42613240, 111889355, 295372835, 783598713, 2088175182, 5587741350, 15009229137, 40458659246, 109416872688, 296810505298 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 3..650

FORMULA

a(n) ~ c * d^n / n^(5/2), where d = A051491 = 2.9557652856519949747148..., c = 0.13932434077355395... . - Vaclav Kotesovec, Sep 07 2014

EXAMPLE

a(5) = 3: .o o-o.  .o o-o.  .o o o.

          .  |/ .  .  |  .  .| |  .

          .o o  .  .o o  .  .o o  .

MAPLE

with(numtheory):

b:= proc(n) option remember; local d, j; `if`(n<=1, n,

      (add(add(d*b(d), d=divisors(j)) *b(n-j), j=1..n-1))/(n-1))

    end:

g:= proc(n) option remember; local k; `if`(n>2, 1, 0)+ b(n)-

      (add(b(k)*b(n-k), k=0..n) -`if`(irem(n, 2)=0, b(n/2), 0))/2

    end:

p:= proc(n, i, t) option remember; `if`(n<t, 0, `if`(n=t, 1,

      `if`(min(i, t)<1, 0, add(binomial(g(i)+j-1, j)*

       p(n-i*j, i-1, t-j), j=0..min(n/i, t)))))

    end:

a:= n-> p(n, n, 3):

seq(a(n), n=3..40);

CROSSREFS

Column k=3 of A215977.

The labeled version is A215853.

Sequence in context: A024505 A005256 A097979 * A319445 A316318 A173216

Adjacent sequences:  A215980 A215981 A215982 * A215984 A215985 A215986

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 29 2012

STATUS

approved

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Last modified August 23 00:50 EDT 2019. Contains 326211 sequences. (Running on oeis4.)