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A209869
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.
2
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
OFFSET
1,16
REFERENCES
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.
LINKS
FORMULA
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.
MAPLE
with(numtheory);
A209869:=proc(i)
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:
A209869(1000);
MATHEMATICA
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}]
CROSSREFS
Sequence in context: A316846 A130241 A130247 * A087839 A106742 A106733
KEYWORD
nonn
AUTHOR
STATUS
approved