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A215985
Number of simple unlabeled graphs on n nodes with exactly 5 connected components that are trees or cycles.
3
1, 1, 3, 6, 13, 26, 55, 112, 238, 510, 1117, 2498, 5712, 13322, 31643, 76455, 187382, 465393, 1168966, 2966298, 7594035, 19597653, 50933434, 133224112, 350477003, 926855665, 2462830565, 6572892862, 17612586165, 47369774428, 127841265076, 346120109957
OFFSET
5,3
LINKS
EXAMPLE
a(7) = 3: .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, 5):
seq(a(n), n=5..40);
CROSSREFS
Column k=5 of A215977.
The labeled version is A215855.
Sequence in context: A320733 A164991 A213255 * A215986 A215987 A215988
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 29 2012
STATUS
approved