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A215987 Number of simple unlabeled graphs on n nodes with exactly 7 connected components that are trees or cycles. 3
1, 1, 3, 6, 13, 26, 56, 115, 246, 530, 1166, 2613, 5982, 13940, 33073, 79760, 195109, 483615, 1212485, 3071358, 7850690, 20231286, 52513864, 137202595, 360578812, 952705531, 2529454122, 6745724961, 18063628118, 48553319703, 130962595786, 354390168855 (list; graph; refs; listen; history; text; internal format)
OFFSET

7,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 7..650

EXAMPLE

a(9) = 3: .o-o o o o.  .o-o o o 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, 7):

seq(a(n), n=7..50);

CROSSREFS

Column k=7 of A215977.

The labeled version is A215857.

Sequence in context: A213255 A215985 A215986 * A215988 A215989 A215980

Adjacent sequences:  A215984 A215985 A215986 * A215988 A215989 A215990

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 29 2012

STATUS

approved

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Last modified September 27 03:01 EDT 2022. Contains 357051 sequences. (Running on oeis4.)