OFFSET
0,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
FORMULA
a(n) ~ 3^(n+1) / (4*n). - Vaclav Kotesovec, Nov 02 2023
MAPLE
with(numtheory):
b:= proc(n) option remember; ceil(add(
phi(d)*2^(n/d)/(2*n), d=divisors(n))+
`if`(n::odd, 2^((n-1)/2), 2^(n/2-1)+2^(n/2-2)))
end:
a:= n-> add(b(n-j)*binomial(n, j), j=0..n):
seq(a(n), n=0..30); # Alois P. Heinz, Jul 17 2017
MATHEMATICA
a29[n_] := If[n == 0, 1, DivisorSum[n, EulerPhi[#]*2^(n/#)&]/(2*n) + If[OddQ[n], 2^((n-1)/2), 2^(n/2-1) + 2^(n/2-2)]]; a[n_] := Sum[Binomial[n, k] * a29[k], {k, 0, n}]; Array[a, 28, 0] (* Jean-François Alcover, Jul 17 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Apr 29 2000
STATUS
approved