OFFSET
1,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..700
FORMULA
a(1) = a(2) = 1, a(n) = 1 + A000055(n) for n>=3.
EXAMPLE
a(5) = 4: .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:
a:= 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:
seq(a(n), n=1..40);
MATHEMATICA
b[n_] := b[n] = If[n <= 1, n, (Sum[Sum[d*b[d], {d, Divisors[j]}]*b[n - j], {j, 1, n - 1}])/(n - 1)];
a[n_] := a[n] = If[n > 2, 1, 0] + b[n] - (Sum[b[k]*b[n - k], {k, 0, n}] - If[Mod[n, 2] == 0, b[n/2], 0])/2;
Array[a, 40] (* Jean-François Alcover, Mar 21 2017, translated from Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 29 2012
STATUS
approved