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 A356098 #10 Jan 18 2023 03:28:59 %S A356098 1,1,1,1,0,0,0,3,0,1,0,0,1,1,1,1,-1,1,-1,0,0,0,0,0,-3,3,-3,0,0,3,3,3, %T A356098 3,0,0,-3,3,3,3,-3,0,-1,0,3,3,3,3,0,-1,1,1,0,-3,3,-3,0,1,1,1,1,-1,0,0, %U A356098 0,0,-1,1,1,1,0,0,0,3,0,1,0,0,1,2,0,3,0,2 %N A356098 A family of triangles T(m), m >= 0, read by triangles and then by rows; triangle T(0) is [1; 1, 1]; for m >= 0, triangle T(m+1) is obtained by replacing each subtriangle [t; u, v] in T(m) by [t; t-u, t-v; u-t, t+u+v, v-t; u, u-v, v-u, v]. %C A356098 We apply the following substitutions to transform T(m) into T(m+1): %C A356098 t %C A356098 / \ %C A356098 / \ %C A356098 t t-u---t-v %C A356098 / \ ___\ / \ / \ %C A356098 / \ / / \ / \ %C A356098 u-----v u-t--t+u+v--v-t %C A356098 / \ / \ / \ %C A356098 / \ / \ / \ %C A356098 u----u-v---v-u----v %C A356098 and: %C A356098 u----u-v---v-u----v %C A356098 \ / \ / \ / %C A356098 \ / \ / \ / %C A356098 u-----v u-t--t+u+v--v-t %C A356098 \ / ___\ \ / \ / %C A356098 \ / / \ / \ / %C A356098 t t-u---t-v %C A356098 \ / %C A356098 \ / %C A356098 t %C A356098 T(m) has 3^m+1 rows. %C A356098 As m gets larger, T(m) exhibits interesting fractal features (see illustrations in Links section). %H A356098 Rémy Sigrist, <a href="/A356098/a356098.png">Colored representation of T(6)</a> (where the color is function of T(6)(n,k)) %H A356098 Rémy Sigrist, <a href="/A356098/a356098_1.png">Representation of the multiples of 2 in T7</a> %H A356098 Rémy Sigrist, <a href="/A356098/a356098_2.png">Representation of the multiples of 5 in T7</a> %H A356098 Rémy Sigrist, <a href="/A356098/a356098.gp.txt">PARI program</a> %H A356098 Rémy Sigrist, <a href="https://arxiv.org/abs/2301.06039">Nonperiodic tilings related to Stern's diatomic series and based on tiles decorated with elements of Fp</a>, arXiv:2301.06039 [math.CO], 2023. %e A356098 Triangle T(0) is: %e A356098 1 %e A356098 1 1 %e A356098 Triangle T(1) is: %e A356098 1 %e A356098 0 0 %e A356098 0 3 0 %e A356098 1 0 0 1 %e A356098 Triangle T(2) is: %e A356098 1 %e A356098 1 1 %e A356098 -1 1 -1 %e A356098 0 0 0 0 %e A356098 0 -3 3 -3 0 %e A356098 0 3 3 3 3 0 %e A356098 0 -3 3 3 3 -3 0 %e A356098 -1 0 3 3 3 3 0 -1 %e A356098 1 1 0 -3 3 -3 0 1 1 %e A356098 1 1 -1 0 0 0 0 -1 1 1 %o A356098 (PARI) See Links section. %Y A356098 See A355855, A356002, A356096 and A356097 for similar sequences. %K A356098 sign,tabl %O A356098 0,8 %A A356098 _Rémy Sigrist_, Jul 26 2022