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A035080 Number of asymmetric connected graphs where every block is a complete graph. 3
1, 1, 0, 0, 0, 0, 1, 3, 7, 21, 60, 168, 472, 1344, 3843, 11104, 32305, 94734, 279708, 831401, 2485877, 7474667, 22589771, 68594611, 209198103, 640591332, 1968920180, 6072766832, 18791062733, 58321579888, 181524367875, 566488767763, 1772261945866, 5557515157647 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..600

FORMULA

G.f.: A(x) = B(x) + C(x) - B(x)*C(x), where B and C are g.f.s of A007561 and A035079, respectively.

a(n) ~ c * d^n / n^(5/2), where d = 3.38201646602027280742981874... (same as for A007561), c = 0.12430588691278777480105... . - Vaclav Kotesovec, Sep 10 2014

MAPLE

g:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,

      add(binomial(b((i-1)$2), j)*g(n-i*j, i-1), j=0..n/i)))

    end:

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,

      add(binomial(g(i$2), j)*b(n-i*j, i-1), j=0..n/i)))

    end:

a:= n-> b((n-1)$2)+g(n$2)-add(b((i-1)$2)*g((n-i)$2), i=0..n):

seq(a(n), n=0..40); # Alois P. Heinz, May 20 2013

MATHEMATICA

g[n_, i_] := g[n, i] = If[n==0, 1, If[i<1, 0, Sum[Binomial[b[i-1, i-1], j]*g[n-i*j, i-1], {j, 0, n/i}]]]; b[n_, i_] := b[n, i] = If[n==0, 1, If[i < 1, 0, Sum[Binomial[g[i, i], j]*b[n-i*j, i-1], {j, 0, n/i}]]]; a[n_] := b[n-1, n-1] + g[n, n] - Sum[b[i-1, i-1]*g[n-i, n-i], {i, 0, n}]; Table[ a[n], {n, 0, 40}] (* Jean-Fran├žois Alcover, Feb 19 2016, after Alois P. Heinz *)

CROSSREFS

Cf. A007561, A035081.

Sequence in context: A091650 A096240 A182887 * A229188 A091486 A056779

Adjacent sequences:  A035077 A035078 A035079 * A035081 A035082 A035083

KEYWORD

nonn

AUTHOR

Christian G. Bower, Nov 15 1998

STATUS

approved

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Last modified December 10 15:13 EST 2016. Contains 279003 sequences.