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A113535 Ascending descending base exponent transform of the tribonacci substitution (A100619).

%I A113535 #18 Jan 03 2019 03:44:19
%S A113535 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 A113535 52,90,101,82,101,88,122,63,81,92,153,110,89,125,110,92,101,155,90,
%U A113535 127,196,142,87,138,207,112,112,135,217,150,124,115,204,245,139,158,189,268,121,155,154
%N A113535 Ascending descending base exponent transform of the tribonacci substitution (A100619).
%C A113535 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 A113535 G. C. Greubel, <a href="/A113535/b113535.txt">Table of n, a(n) for n = 1..500</a>
%H A113535 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 A113535 a(n) = Sum_{k=1..n} A100619(k)^(A100619(n-k-1)). - _G. C. Greubel_, May 18 2017
%e A113535 a(1) = A100619(1)^A100619(1) = 1^1 = 1.
%e A113535 a(2) = A100619(1)^A100619(2) + A100619(2)^A100619(1) = 1^2 + 2^1 = 3.
%e A113535 a(3) = 1^3 + 2^2 + 3^1 = 8.
%e A113535 a(4) = 1^1 + 2^3 + 3^2 + 1^1 = 19.
%e A113535 a(5) = 1^1 + 2^1 + 3^3 + 1^2 + 1^1 = 32.
%e A113535 a(6) = 1^1 + 2^1 + 3^1 + 1^3 + 1^2 + 1^1 = 9.
%e A113535 a(7) = 1^2 + 2^1 + 3^1 + 1^1 + 1^3 + 1^2 + 2^1 = 11.
%e A113535 a(8) = 1^1 + 2^2 + 3^1 + 1^1 + 1^1 + 1^3 + 2^2 + 1^1 = 16.
%e A113535 a(9) = 1^1 + 2^1 + 3^2 + 1^1 + 1^1 + 1^1 + 2^3 + 1^2 + 2^1 = 26.
%e A113535 a(10) = 1^1 + 2^2 + 3^1 + 1^2 + 1^1 + 1^1 + 2^1 + 1^3 + 2^2 + 1^1 = 19.
%e A113535 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 A113535 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 A113535 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 A113535 Cf. A100619, A092782, A103269, A113320, A005408, A113122, A113153, A113154, A113336, A113271, A113258, A113257, A113231, A087316, A113208, A113498.
%K A113535 easy,nonn
%O A113535 1,2
%A A113535 _Jonathan Vos Post_, Jan 13 2006
%E A113535 Terms a(13) to a(50) from _G. C. Greubel_, May 18 2017
%E A113535 Terms a(51) onward added by _G. C. Greubel_, Jan 03 2019