This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A371636 #15 Apr 03 2024 10:07:01
%S A371636 0,1,4,13,19,25,40,103,112,121,154,214,364,442,505,595,673,763,826,
%T A371636 913,1003,1093,1144,1369,1621,1915,2167,2392,2776,3028,3280,3628,4420,
%U A371636 4996,5668,6244,7036,8203,9022,9841,10459,10594,11782,12304,13411,13627,14419
%N A371636 For any number k >= 0, let T_k be the triangle with values in {-1, 0, +1} whose base corresponds to the balanced ternary expansion of k (without leading zeros) and other values, say t above u and v, satisfy t+u+v = 0 mod 3; this sequence lists the numbers k such that T_k has 3-fold rotational symmetry.
%C A371636 This sequence is a variant of A334556 and A361818.
%C A371636 This sequence is infinite as it contains A003462.
%C A371636 Empirically, for any w > 0, there are A127975(w-1) terms with w balanced ternary digits (ignoring leading zeros).
%C A371636 If k is a term then A338246(k) is also a term.
%H A371636 Rémy Sigrist, <a href="/A371636/a371636.png">Triangles illustrating initial terms</a> (blue, gray and red respectively denote -1's, 0's and 1's)
%H A371636 Rémy Sigrist, <a href="/A371636/a371636.gp.txt">PARI program</a>
%H A371636 <a href="/index/X#XOR-triangles">Index entries for sequences related to XOR-triangles</a>
%e A371636 The balanced ternary expansion of 595 is "1T11001" (where T denotes -1), and the corresponding triangle T_595 is as follows:
%e A371636 1
%e A371636 T 0
%e A371636 1 0 0
%e A371636 1 1 T 1
%e A371636 0 T 0 1 1
%e A371636 0 0 1 T 0 T
%e A371636 1 T 1 1 0 0 1
%e A371636 As this triangle has 3-fold rotational symmetry, 595 belongs to the sequence.
%o A371636 (PARI) \\ See Links section.
%Y A371636 Cf. A003462, A127975, A334556, A338246, A361818, A371635.
%K A371636 nonn,base
%O A371636 1,3
%A A371636 _Rémy Sigrist_, Mar 30 2024