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A298407
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a(n) = 2*a(n-1) - a(n-3) + a(floor(n/2)) + a(floor(n/3)) + ... + a(floor(n/n)), where a(0) = 1, a(1) = 2, a(2) = 3.
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3
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1, 2, 3, 9, 23, 52, 113, 223, 431, 794, 1442, 2532, 4433, 7589, 12924, 21730, 36411, 60440, 100125, 164816, 270863, 443390, 724846, 1181713, 1925113, 3130488, 5087530, 8258585, 13400782, 21728136, 35221342, 57065559, 92441545, 149701409, 242400952, 392424193
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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] = 2*a[n - 1] - a[n - 3] + Sum[a[Floor[n/k]], {k, 2, n}];
Table[a[n], {n, 0, 90}] (* A298407 *)
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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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