OFFSET
0,4
COMMENTS
a(2^n) = Product_{k=1..n} A003095(k). - Michael Somos, Dec 20 2018
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..5654
FORMULA
a(1) = a(2) = 1, a(3*2^m + k) = A003095(m+2) * a(n - 2*2^m) where 0 <= k < 3*2^m. - Michael Somos, Dec 20 2018
a(n) = Sum_{k=0..n} (A309049(n,k)-A309049(n-1,k)) for n > 0, a(0) = 1. - Alois P. Heinz, Jul 12 2019
MAPLE
b:= proc(n) option remember; `if`(n=0, 1, (g-> (f->
1+b(f)*b(n-1-f))(min(g-1, n-g/2)))(2^ilog2(n)))
end:
a:= n-> b(n)-`if`(n=0, 0, b(n-1)):
seq(a(n), n=0..45); # Alois P. Heinz, Jul 12 2019
MATHEMATICA
a[ n_] := If[ n < 3, Boole[n > 0], With[{m = BitLength[Quotient[n, 3]] - 1}, Nest[#^2 + 1 &, 2, m] a[n - 2 2^m]]]; (* Michael Somos, Dec 20 2018 *)
PROG
(PARI) {a(n) = if( n<3, n>0, my(m = #binary(n\3)-1, t = 2); for(i=1, m, t = t^2+1); t*a(n - 2*2^m))}; /* Michael Somos, Dec 20 2018 */
CROSSREFS
KEYWORD
nonn
AUTHOR
Endi Begeja (andy.bege(AT)libero.it), Nov 29 2009
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Jul 12 2019
STATUS
approved