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A209869
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a(n) = a(a(n-1)) + a(n - a(n-2)) - a(a(n-3)) + a(a(n-5)), with a(1) to a(15) = 1.
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2
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11
(list;
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listen;
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internal format)
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OFFSET
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1,16
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REFERENCES
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G. Balzarotti and P. P. Lava, 103 curiosità matematiche, Hoepli, 2010, p. 275.
Clifford A. Pickover, The Crying of Fractal Batrachion 1,489. Chaos and Graphics, Comput. and Graphics, vol. 19, No. 4, pages 611-615, 1995.
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LINKS
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FORMULA
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a(n) = a(a(n-1)) + a(n-a(n-2)) - a(a(n-3)) + a(a(n-5)), with a(n) = 1 for n <= 15.
lim_{n->oo} a(n)/n = 1/4.
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MAPLE
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with(numtheory);
local a, n;
a:=array(1..10000); for n from 1 to 15 do a[n]:=1; print(a[n]); od;
for n from 16 to i do
a[n]:=a[a[n-1]]+a[n-a[n-2]]-a[a[n-3]]+a[a[n-5]]; print(a[n]);
od; end:
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MATHEMATICA
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a[n_Integer] := a[n] = If[n < 16, 1, a[a[n - 1]] + a[n - a[n - 2]] - a[a[n - 3]] + a[a[n - 5]]]; Table[a[n], {n, 500}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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