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%I #18 Jan 03 2019 03:44:19
%S 1,3,8,19,32,9,11,16,26,19,29,24,47,70,28,31,58,89,35,50,65,108,65,51,
%T 52,90,101,82,101,88,122,63,81,92,153,110,89,125,110,92,101,155,90,
%U 127,196,142,87,138,207,112,112,135,217,150,124,115,204,245,139,158,189,268,121,155,154
%N Ascending descending base exponent transform of the tribonacci substitution (A100619).
%C Sirvent comments that in spite of the similarity of this map to the one in A092782, the two sequences have very different properties. They have different complexities, different Rauzy fractals, etc.
%H G. C. Greubel, <a href="/A113535/b113535.txt">Table of n, a(n) for n = 1..500</a>
%H V. F. Sirvent, <a href="http://dx.doi.org/10.1016/S0893-9659(98)00121-9">Semigroups and the self-similar structure of the flipped tribonacci substitution</a>, Applied Math. Letters, 12 (1999), 25-29. [Contains many further references.]
%F a(n) = Sum_{k=1..n} A100619(k)^(A100619(n-k-1)). - _G. C. Greubel_, May 18 2017
%e a(1) = A100619(1)^A100619(1) = 1^1 = 1.
%e a(2) = A100619(1)^A100619(2) + A100619(2)^A100619(1) = 1^2 + 2^1 = 3.
%e a(3) = 1^3 + 2^2 + 3^1 = 8.
%e a(4) = 1^1 + 2^3 + 3^2 + 1^1 = 19.
%e a(5) = 1^1 + 2^1 + 3^3 + 1^2 + 1^1 = 32.
%e a(6) = 1^1 + 2^1 + 3^1 + 1^3 + 1^2 + 1^1 = 9.
%e a(7) = 1^2 + 2^1 + 3^1 + 1^1 + 1^3 + 1^2 + 2^1 = 11.
%e a(8) = 1^1 + 2^2 + 3^1 + 1^1 + 1^1 + 1^3 + 2^2 + 1^1 = 16.
%e a(9) = 1^1 + 2^1 + 3^2 + 1^1 + 1^1 + 1^1 + 2^3 + 1^2 + 2^1 = 26.
%e a(10) = 1^1 + 2^2 + 3^1 + 1^2 + 1^1 + 1^1 + 2^1 + 1^3 + 2^2 + 1^1 = 19.
%e a(11) = 1^2 + 2^1 + 3^2 + 1^1 + 1^2 + 1^1 + 2^1 + 1^1 + 2^3 + 1^2 + 2^1 = 29.
%e a(12) = 1^3 + 2^2 + 3^1 + 1^2 + 1^1 + 1^2 + 2^1 + 1^1 + 2^1+ 1^3 + 2^2 + 3^1 = 24.
%t A100619:= Nest[Function[l, {Flatten[(l /. {1 -> {1, 2}, 2 -> {3, 1}, 3 -> {1}})]}], {1}, 8][[1]]; Table[Sum[(A100619[[k]])^(A100619[[n-k+1]]), {k, 1, n}], {n, 1, 100}] (* _G. C. Greubel_, May 18 2017 *)
%Y Cf. A100619, A092782, A103269, A113320, A005408, A113122, A113153, A113154, A113336, A113271, A113258, A113257, A113231, A087316, A113208, A113498.
%K easy,nonn
%O 1,2
%A _Jonathan Vos Post_, Jan 13 2006
%E Terms a(13) to a(50) from _G. C. Greubel_, May 18 2017
%E Terms a(51) onward added by _G. C. Greubel_, Jan 03 2019
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