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A215984 Number of simple unlabeled graphs on n nodes with exactly 4 connected components that are trees or cycles. 3
1, 1, 3, 6, 13, 25, 53, 106, 224, 475, 1037, 2315, 5302, 12382, 29495, 71450, 175618, 437272, 1101000, 2799768, 7181703, 18565546, 48326482, 126581749, 333424119, 882765486, 2348114866, 6272676477, 16822741588, 45281587081, 122295734356, 331331765694 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 4..650

EXAMPLE

a(6) = 3: .o-o o.  .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, 4):

seq(a(n), n=4..40);

CROSSREFS

Column k=4 of A215977.

The labeled version is A215854.

Sequence in context: A005407 A005116 A121349 * A074890 A244704 A032198

Adjacent sequences:  A215981 A215982 A215983 * A215985 A215986 A215987

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 29 2012

STATUS

approved

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Last modified February 21 02:02 EST 2020. Contains 332086 sequences. (Running on oeis4.)