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A215984 Number of simple unlabeled graphs on n nodes with exactly 4 connected components that are trees or cycles.

%I A215984 #8 Dec 04 2014 06:54:29
%S A215984 1,1,3,6,13,25,53,106,224,475,1037,2315,5302,12382,29495,71450,175618,
%T A215984 437272,1101000,2799768,7181703,18565546,48326482,126581749,333424119,
%U A215984 882765486,2348114866,6272676477,16822741588,45281587081,122295734356,331331765694
%N A215984 Number of simple unlabeled graphs on n nodes with exactly 4 connected components that are trees or cycles.
%H A215984 Alois P. Heinz, <a href="/A215984/b215984.txt">Table of n, a(n) for n = 4..650</a>
%e A215984 a(6) = 3: .o-o o.  .o-o o.  .o o o.
%e A215984           .|/   .  .|    .  .| |  .
%e A215984           .o o o.  .o o o.  .o o o.
%p A215984 with(numtheory):
%p A215984 b:= proc(n) option remember; local d, j; `if`(n<=1, n,
%p A215984       (add(add(d*b(d), d=divisors(j)) *b(n-j), j=1..n-1))/(n-1))
%p A215984     end:
%p A215984 g:= proc(n) option remember; local k; `if`(n>2, 1, 0)+ b(n)-
%p A215984       (add(b(k)*b(n-k), k=0..n) -`if`(irem(n, 2)=0, b(n/2), 0))/2
%p A215984     end:
%p A215984 p:= proc(n, i, t) option remember; `if`(n<t, 0, `if`(n=t, 1,
%p A215984       `if`(min(i, t)<1, 0, add(binomial(g(i)+j-1, j)*
%p A215984        p(n-i*j, i-1, t-j), j=0..min(n/i,t)))))
%p A215984     end:
%p A215984 a:= n-> p(n, n, 4):
%p A215984 seq(a(n), n=4..40);
%Y A215984 Column k=4 of A215977.
%Y A215984 The labeled version is A215854.
%K A215984 nonn
%O A215984 4,3
%A A215984 _Alois P. Heinz_, Aug 29 2012