A215989 Number of simple unlabeled graphs on n nodes with exactly 9 connected components that are trees or cycles.

1, 1, 3, 6, 13, 26, 56, 115, 247, 533, 1174, 2633, 6031, 14055, 33343, 80386, 196569, 487017, 1220491, 3090331, 7896160, 20341323, 52783053, 137867631, 362237861, 956881142, 2540051927, 6772828374, 18133435767, 48734282113, 131434508449, 355627568994

Offset

9,3

Links

Alois P. Heinz, Table of n, a(n) for n = 9..650

Example

a(11) = 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 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, 9):
seq(a(n), n=9..50);

Crossrefs

Column k=9 of A215977.

The labeled version is A215859.

Sequence in context: A215986 A215987 A215988 * A215980 A215979 A273226

Adjacent sequences: A215986 A215987 A215988 * A215990 A215991 A215992

Keyword

nonn

Author

Alois P. Heinz, Aug 29 2012

Status

approved