A035080 Number of asymmetric connected graphs where every block is a complete graph.

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

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-François Alcover, Feb 19 2016, after Alois P. Heinz *)

Crossrefs

Cf. A007561, A035081.

Sequence in context: A091650 A096240 A182887 * A229188 A345955 A091486

Adjacent sequences: A035077 A035078 A035079 * A035081 A035082 A035083

Keyword

nonn

Author

Christian G. Bower, Nov 15 1998

Status

approved