A215988 Number of simple unlabeled graphs on n nodes with exactly 8 connected components that are trees or cycles.

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

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