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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. 1
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; graph; refs; listen; history; text; internal format)
OFFSET

1,16

COMMENTS

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.

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, N0.4, pages 611-615, 1995.

LINKS

Paolo P. Lava, Table of n, a(n) for n = 1..10000

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.

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

Cf. A107293.

Sequence in context: A316846 A130241 A130247 * A087839 A106742 A106733

Adjacent sequences:  A209866 A209867 A209868 * A209870 A209871 A209872

KEYWORD

nonn

AUTHOR

Paolo P. Lava and Roger L. Bagula, Mar 14 2012

STATUS

approved

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Last modified December 8 08:49 EST 2019. Contains 329862 sequences. (Running on oeis4.)