OFFSET
0,9
COMMENTS
Lim_{n->infinity} a(n+1)/a(n) = 2. Contrast with Fibonacci sequence. Also a(n+1)/a(n) = 2 iff n+1 >= 8 is a cube.
Up to a(26) = 10946, but not beyond, the sequence consists of the Fibonacci numbers A000045(0..21). - M. F. Hasler, May 10 2017
LINKS
Robert Israel, Table of n, a(n) for n = 0..3345
FORMULA
a(n) = Sum_{k=1..floor(n^(1/3))} a(n-k) for n >= 2; a(0)=0; a(1)=1.
EXAMPLE
a(27) = a(24) + a(25) + a(26) = 4181 + 6765 + 10946 = 21892.
MAPLE
f:= proc(n) option remember;
add(procname(n-k), k=1..floor(n^(1/3)))
end proc:
f(0):= 0: f(1):= 1:
map(f, [$0..50]); # Robert Israel, Dec 16 2018
MATHEMATICA
a[n_] := a[n] = If[n < 2, n, Sum[a[n - k], {k, Floor[n^(1/3)]}]]; Array[a, 43, 0] (* Michael De Vlieger, May 10 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Rick L. Shepherd, Sep 04 2007
EXTENSIONS
Incorrect g.f. and programs deleted by Colin Barker, Dec 17 2018
STATUS
approved