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%I #27 Dec 17 2018 12:03:08
%S 0,1,1,1,1,1,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,
%T 4181,6765,10946,21892,39603,72441,133936,245980,452357,832273,
%U 1530610,2815240,5178123,9523973,17517336,32219432,59260741,108997509,200477682
%N a(0)=0; a(1)=1; a(n) = Sum_{k=1..floor(n^(1/3))} a(n-k) for n >= 2.
%C 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.
%C Up to a(26) = 10946, but not beyond, the sequence consists of the Fibonacci numbers A000045(0..21). - _M. F. Hasler_, May 10 2017
%H Robert Israel, <a href="/A132916/b132916.txt">Table of n, a(n) for n = 0..3345</a>
%F a(n) = Sum_{k=1..floor(n^(1/3))} a(n-k) for n >= 2; a(0)=0; a(1)=1.
%e a(27) = a(24) + a(25) + a(26) = 4181 + 6765 + 10946 = 21892.
%p f:= proc(n) option remember;
%p add(procname(n-k),k=1..floor(n^(1/3)))
%p end proc:
%p f(0):= 0: f(1):= 1:
%p map(f, [$0..50]); # _Robert Israel_, Dec 16 2018
%t 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 *)
%Y Cf. A000045, A132915.
%K nonn
%O 0,9
%A _Rick L. Shepherd_, Sep 04 2007
%E Incorrect g.f. and programs deleted by _Colin Barker_, Dec 17 2018
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