A132916 a(0)=0; a(1)=1; a(n) = Sum_{k=1..floor(n^(1/3))} a(n-k) for n >= 2.

0, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 21892, 39603, 72441, 133936, 245980, 452357, 832273, 1530610, 2815240, 5178123, 9523973, 17517336, 32219432, 59260741, 108997509, 200477682

Offset: 0

Author

Rick L. Shepherd, Sep 04 2007

Keywords

• nonn

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

Examples

			a(27) = a(24) + a(25) + a(26) = 4181 + 6765 + 10946 = 21892.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..3345

Crossrefs

Cf. A000045, A132915.

Programs

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 *)

Formula

a(n) = Sum_{k=1..floor(n^(1/3))} a(n-k) for n >= 2; a(0)=0; a(1)=1.

Extensions

Incorrect g.f. and programs deleted by Colin Barker, Dec 17 2018