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A132916
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a(0)=0; a(1)=1; a(n) = Sum a(n-k), k= 1 ... [n^(1/3)] for n>=2.
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,9
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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.
Contribution from Paul Barry (pbarry(AT)wit.ie), Nov 03 2010: (Start)
The sequence 1,1,1,2,3,5,... has g.f. 1/(1-x/(1-x^2)), INVERT transform of A059841.
It is an eigensenquence for the sequence array for A059841. (End)
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FORMULA
| a(n) = sum a(n-k), k= 1 ... [n^(1/3)] for n>=2; a(0)=0; a(1)=1.
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EXAMPLE
| a(27) = a(24) + a(25) + a(26) = 4181 + 6765 + 10946 = 21892.
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CROSSREFS
| Cf. A132915.
Sequence in context: A039834 A000045 A020695 * A177194 A177247 A069041
Adjacent sequences: A132913 A132914 A132915 * A132917 A132918 A132919
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KEYWORD
| nonn
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AUTHOR
| Rick L. Shepherd (rshepherd2(AT)hotmail.com), Sep 04 2007
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