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A038150 Array of numbers used in exotic ternary numeration system, read by antidiagonals.

%I A038150 #33 Jan 29 2022 12:23:55
%S A038150 1,2,3,4,6,8,5,11,16,21,7,14,29,42,55,9,19,37,76,110,144,10,24,50,97,
%T A038150 199,288,377,12,27,63,131,254,521,754,987,13,32,71,165,343,665,1364,
%U A038150 1974,2584,15,35,84,186,432,898,1741,3571,5168,6765,17,40,92,220,487
%N A038150 Array of numbers used in exotic ternary numeration system, read by antidiagonals.
%H A038150 A. S. Fraenkel, <a href="https://doi.org/10.1016/S0304-3975(00)00062-1">Recent results and questions in combinatorial game complexities</a>, Theoretical Computer Science, vol. 249, no. 2 (2000), 265-288.
%H A038150 A. S. Fraenkel, <a href="https://doi.org/10.1016/S0304-3975(01)00070-6">Arrays, numeration systems and Frankenstein games</a>, Theoret. Comput. Sci. 282 (2002), 271-284; <a href="http://www.wisdom.weizmann.ac.il/~fraenkel/Papers/ans1.ps">preprint</a>.
%F A038150 For n >= 0, A_0^n is the least nonnegative integer not in {A_j^n: 0 <= i < n, j >= 0, A_1^n = 2A_0^n + n, A_j^n = 3A_{j-1}^n - A_{j-2}^n (j >= 2).
%F A038150 a(n,k) = F(2k)*n + F(2k+1)*A026351(n). - _Charlie Neder_, Feb 07 2019
%e A038150 Top left corner of array:
%e A038150   1,  3,  8, 21,  55, ...
%e A038150   2,  6, 16, 42, 110, ...
%e A038150   4, 11, 29, 76, 199, ...
%e A038150   5, 14, 37, 97, 254, ...
%t A038150 t[n_, 1] := Floor[(n - 1) GoldenRatio] + 1; t[n_, j_] := Floor[ GoldenRatio^2 t[n, j - 1]] + 1; Table[ t[n - m + 1, m], {n, 11}, {m, n}] // Flatten (* _Birkas Gyorgy_, Apr 15 2011; modified by _Robert G. Wilson v_, Apr 15 2011 *)
%Y A038150 Rows give A001906, A025169, A002878.
%Y A038150 Columns give A026351, A047924, A047925.
%Y A038150 Main diagonal gives A047923.
%Y A038150 Cf. A026351, A035506.
%K A038150 nonn,tabl,nice,easy
%O A038150 0,2
%A A038150 _Aviezri S. Fraenkel_
%E A038150 More terms from _Naohiro Nomoto_, Jun 07 2001