A215985 Number of simple unlabeled graphs on n nodes with exactly 5 connected components that are trees or cycles.

1, 1, 3, 6, 13, 26, 55, 112, 238, 510, 1117, 2498, 5712, 13322, 31643, 76455, 187382, 465393, 1168966, 2966298, 7594035, 19597653, 50933434, 133224112, 350477003, 926855665, 2462830565, 6572892862, 17612586165, 47369774428, 127841265076, 346120109957

Offset

5,3

Links

Alois P. Heinz, Table of n, a(n) for n = 5..650

Example

a(7) = 3: .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, 5):
seq(a(n), n=5..40);

Crossrefs

Column k=5 of A215977.

The labeled version is A215855.

Sequence in context: A320733 A164991 A213255 * A215986 A215987 A215988

Adjacent sequences: A215982 A215983 A215984 * A215986 A215987 A215988

Keyword

nonn

Author

Alois P. Heinz, Aug 29 2012

Status

approved