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

Author

Alois P. Heinz, Aug 29 2012

Keywords

• nonn

Examples

			a(7) = 3: .o-o o o.  .o-o o o.  .o o o o.
          .|/     .  .|      .  .| |    .
          .o o o  .  .o o o  .  .o o o  .
		

Links

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

Crossrefs

Column k=5 of A215977.

The labeled version is A215855.

Programs

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