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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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1
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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
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OFFSET
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1,16
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COMMENTS
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Based on A107293: (thought to be the 5th order minimal Pisot) a[0] = 1; a[1] = 1; a[2] = 2; a[3] = 2; a[4] = 3; a[n_Integer] := a[n] = a[n - 1] + a[n - 2] - a[n - 3] + a[n - 5]; Table[a[n], {n, 0, 50}].
This sequence has the unique Batrachion limit of 1/4 instead of the usual 1/2: Limit[a[n]/n-1/4,n->Infinity]=0.
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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, N0.4, pages 611-615, 1995.
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LINKS
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Paolo P. Lava, Table of n, a(n) for n = 1..10000
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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.
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MAPLE
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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);
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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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Cf. A107293.
Sequence in context: A316846 A130241 A130247 * A087839 A106742 A106733
Adjacent sequences: A209866 A209867 A209868 * A209870 A209871 A209872
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KEYWORD
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nonn
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AUTHOR
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Paolo P. Lava and Roger L. Bagula, Mar 14 2012
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STATUS
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approved
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