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A298357
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a(n) = a(n-1) + a(n-2) + a([n/2]) + a([n/3]) + ... + a([n/n]), where a(0) = 1, a(1) = 2, a(2) = 3.
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2
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1, 2, 3, 9, 19, 37, 74, 131, 238, 410, 710, 1184, 2014, 3320, 5516, 9044, 14888, 24262, 39698, 64510, 105089, 170545, 277057, 449027, 728502, 1179967, 1912216, 3096110, 5014519, 8116824, 13141430, 21268343, 34425826, 55710704, 90162442, 145899135, 236104060
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OFFSET
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0,2
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COMMENTS
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a(n)/a(n-1) -> (1 + sqrt(5))/2, the golden ratio (A001622), so that (a(n)) has the growth rate of the Fibonacci numbers (A000045). See A298338 for a guide to related sequences.
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LINKS
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MATHEMATICA
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a[0] = 1; a[1] = 2; a[2] = 3;
a[n_] := a[n] = a[n - 1] + a[n - 2] + Sum[a[Floor[n/k]], {k, 2, n}];
Table[a[n], {n, 0, 30}] (* A298357 *)
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PROG
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(Python)
from functools import lru_cache
@lru_cache(maxsize=None)
if n <= 2:
return n+1
k1 = n//j
while k1 > 1:
j2 = n//k1 + 1
j, k1 = j2, n//j2
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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