A215987 Number of simple unlabeled graphs on n nodes with exactly 7 connected components that are trees or cycles.

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

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