OFFSET
0,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..250
FORMULA
G.f.: Product_{k>=1} (1-x^k)/(1-16*x^k). - Alois P. Heinz, Nov 03 2012
MAPLE
with(numtheory):
b:= proc(n) b(n):= add(phi(d)*16^(n/d), d=divisors(n))/n-1 end:
a:= proc(n) a(n):= `if`(n=0, 1,
add(add(d*b(d), d=divisors(j)) *a(n-j), j=1..n)/n)
end:
seq(a(n), n=0..30); # Alois P. Heinz, Nov 03 2012
MATHEMATICA
b[n_] := Sum[EulerPhi[d]*16^(n/d), {d, Divisors[n]}]/n-1; a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d*b[d], {d, Divisors[j]}]*a[n-j], {j, 1, n}]/n]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Feb 17 2014, after Alois P. Heinz *)
PROG
(Magma) /* The program does not work for n>6: */ [1] cat [NumberOfClasses(GL(n, 16)) : n in [1..6]];
(PARI)
N=66; x='x+O('x^N);
gf=prod(n=1, N, (1-x^n)/(1-16*x^n) );
v=Vec(gf)
/* Joerg Arndt, Jan 24 2013 */
CROSSREFS
KEYWORD
nonn
AUTHOR
Klaus Brockhaus, Nov 23 2010
EXTENSIONS
More terms from Alois P. Heinz, Nov 03 2012
MAGMA code edited by Vincenzo Librandi, Jan 24 2013
STATUS
approved