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A215986 Number of simple unlabeled graphs on n nodes with exactly 6 connected components that are trees or cycles. 3
1, 1, 3, 6, 13, 26, 56, 114, 244, 524, 1152, 2578, 5902, 13750, 32637, 78745, 192755, 478071, 1199357, 3039832, 7774296, 20043911, 52049890, 136041966, 357650346, 945253939, 2510351950, 6696412901, 17935526721, 48218592753, 130083292745, 352068892155 (list; graph; refs; listen; history; text; internal format)
OFFSET

6,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 6..650

EXAMPLE

a(8) = 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.

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, 6):

seq(a(n), n=6..40);

CROSSREFS

Column k=6 of A215977.

The labeled version is A215856.

Sequence in context: A164991 A213255 A215985 * A215987 A215988 A215989

Adjacent sequences:  A215983 A215984 A215985 * A215987 A215988 A215989

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 29 2012

STATUS

approved

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Last modified September 29 18:39 EDT 2022. Contains 357090 sequences. (Running on oeis4.)