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A215988 Number of simple unlabeled graphs on n nodes with exactly 8 connected components that are trees or cycles. 3
1, 1, 3, 6, 13, 26, 56, 115, 247, 532, 1172, 2627, 6017, 14020, 33263, 80196, 196133, 485993, 1218103, 3084686, 7882748, 20309036, 52704689, 137675229, 361761187, 955688561, 2537043121, 6765174365, 18113821981, 48683671360, 131303094976, 355284353448 (list; graph; refs; listen; history; text; internal format)
OFFSET

8,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 8..650

EXAMPLE

a(10) = 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 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, 8):

seq(a(n), n=8..50);

CROSSREFS

Column k=8 of A215977.

The labeled version is A215858.

Sequence in context: A215985 A215986 A215987 * A215989 A215980 A215979

Adjacent sequences:  A215985 A215986 A215987 * A215989 A215990 A215991

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 29 2012

STATUS

approved

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Last modified September 25 12:12 EDT 2022. Contains 356984 sequences. (Running on oeis4.)