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A282728 Irregular triangle read by rows: row n gives "digits" d_1, d_2, d_3, ... of the 3-expansion of A282720(n).

%I A282728 #33 Feb 25 2025 13:12:00
%S A282728 1,3,6,2,3,2,7,4,6,4,-2,-7,2,2,3,2,2,8,2,4,9,6,-2,-1,4,4,6,4,-6,2,1,4,
%T A282728 -2,-4,-9,4,-2,-2,-8,2,2,2,3,2,2,2,9,2,2,4,12,2,6,-2,5,2,4,6,9,6,-6,4,
%U A282728 8,6,-2,0,-3,6,2,-4,-15,4,4,4,6,4,-6,-2,4,15,4,-6,2,0,3
%N A282728 Irregular triangle read by rows: row n gives "digits" d_1, d_2, d_3, ... of the 3-expansion of A282720(n).
%H A282728 Julien Leroy, Michel Rigo, and Manon Stipulanti, <a href="https://doi.org/10.37236/6581">Behavior of Digital Sequences Through Exotic Numeration Systems</a>, Electronic Journal of Combinatorics 24(1) (2017), #P1.44. See Lemma 8 p.5 and Table 1 p. 8.
%H A282728 Julien Leroy, Michel Rigo, and Manon Stipulanti, <a href="https://arxiv.org/abs/1705.10065">Counting Subwords Occurrences in Base-b Expansions</a>, arXiv:1705.10065 [math.CO], 2017.
%H A282728 Julien Leroy, Michel Rigo, and Manon Stipulanti, <a href="http://math.colgate.edu/~integers/sjs13/sjs13.Abstract.html">Counting Subwords Occurrences in Base-b Expansions</a>, Integers, Electronic Journal of Combinatorial Number Theory 18A (2018), #A13.
%H A282728 Manon Stipulanti, <a href="https://arxiv.org/abs/1801.03287">Convergence of Pascal-Like Triangles in Parry-Bertrand Numeration Systems</a>, arXiv:1801.03287 [math.CO], 2018.
%e A282728 Triangle begins:
%e A282728   1;
%e A282728   3;
%e A282728   6;
%e A282728   2,  3;
%e A282728   2,  7;
%e A282728   4,  6;
%e A282728   4, -2, -7;
%e A282728   ...
%o A282728 (PARI) add(v, w) = v = Vecrev(v); w = Vecrev(w); my(z = if (#v == #w, v+w, if (#v < #w, Vec(v,#w) + w, Vec(w, #v) + v))); Vecrev(z);
%o A282728 row(n) = if (n==0, return([])); if (n==1, return([1])); my(e = logint(n, 2), r = n-2^e); if (r <= 2^(e-1), add(2*digits(3^(e-1), 3), add(a(2^(e-1)+r), a(r))), add(4*digits(3^e, 3), add(-digits(2*3^(e-1), 3), add(-a(2^(e-1)+2^e-r), -a(2^e-r))))); \\ _Michel Marcus_, Feb 25 2025
%Y A282728 Cf. A282720.
%K A282728 sign,tabf
%O A282728 1,2
%A A282728 _N. J. A. Sloane_, Mar 03 2017
%E A282728 More terms from _Michel Marcus_, Feb 25 2025