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A215986 Number of simple unlabeled graphs on n nodes with exactly 6 connected components that are trees or cycles.

%I A215986 #7 Dec 04 2014 07:12:41
%S A215986 1,1,3,6,13,26,56,114,244,524,1152,2578,5902,13750,32637,78745,192755,
%T A215986 478071,1199357,3039832,7774296,20043911,52049890,136041966,357650346,
%U A215986 945253939,2510351950,6696412901,17935526721,48218592753,130083292745,352068892155
%N A215986 Number of simple unlabeled graphs on n nodes with exactly 6 connected components that are trees or cycles.
%H A215986 Alois P. Heinz, <a href="/A215986/b215986.txt">Table of n, a(n) for n = 6..650</a>
%e A215986 a(8) = 3: .o-o o o.  .o-o o o.  .o o o o.
%e A215986           .|/     .  .|      .  .| |    .
%e A215986           .o o o o.  .o o o o.  .o o o o.
%p A215986 with(numtheory):
%p A215986 b:= proc(n) option remember; local d, j; `if`(n<=1, n,
%p A215986       (add(add(d*b(d), d=divisors(j)) *b(n-j), j=1..n-1))/(n-1))
%p A215986     end:
%p A215986 g:= proc(n) option remember; local k; `if`(n>2, 1, 0)+ b(n)-
%p A215986       (add(b(k)*b(n-k), k=0..n) -`if`(irem(n, 2)=0, b(n/2), 0))/2
%p A215986     end:
%p A215986 p:= proc(n, i, t) option remember; `if`(n<t, 0, `if`(n=t, 1,
%p A215986       `if`(min(i, t)<1, 0, add(binomial(g(i)+j-1, j)*
%p A215986        p(n-i*j, i-1, t-j), j=0..min(n/i,t)))))
%p A215986     end:
%p A215986 a:= n-> p(n, n, 6):
%p A215986 seq(a(n), n=6..40);
%Y A215986 Column k=6 of A215977.
%Y A215986 The labeled version is A215856.
%K A215986 nonn
%O A215986 6,3
%A A215986 _Alois P. Heinz_, Aug 29 2012