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 A356245 #12 Jan 18 2023 03:29:04 %S A356245 1,1,1,1,1,2,2,1,2,3,3,2,2,3,3,2,1,2,2,1,1,3,3,2,4,4,2,3,3,1,3,5,6,5, %T A356245 7,7,5,6,5,3,3,6,7,5,8,8,5,7,6,3,2,5,5,3,6,6,3,5,5,2,4,7,8,6,9,9,6,8, %U A356245 7,4,4,7,8,6,9,9,6,8,7,4,2,5,5,3,6,6,3,5,5,2 %N A356245 A family of squares A(m), m >= 0, read by squares and then by rows; A(0) is [1, 1; 1, 1]; for m >= 0, square A(m+1) is obtained by replacing each subsquare [t, u; v, w] by [t, t+u, t+u, u; t+v, t+u+v, t+u+w, u+w; t+v, t+v+w, u+v+w, u+w; v, v+w, v+w, w] in A(m). %C A356245 We apply the following substitutions to transform A(m) into A(m+1): %C A356245 t----t+u---t+u----u %C A356245 | | | | %C A356245 | | | | %C A356245 t-----u t+v--t+u+v-t+u+w--u+w %C A356245 | | ___\ | | | | %C A356245 | | / | | | | %C A356245 v-----w t+v--t+v+w-u+v+w--u+w %C A356245 | | | | %C A356245 | | | | %C A356245 v----v+w---v+w----w %C A356245 A(m) has 3^m+1 rows. %C A356245 As m gets larger, A(m) exhibits interesting fractal features (see illustrations in Links section). %H A356245 Rémy Sigrist, <a href="/A356245/a356245.png">Representation of the multiples of 2 in T(6)</a> %H A356245 Rémy Sigrist, <a href="/A356245/a356245_1.png">Representation of the multiples of 3 in T(6)</a> %H A356245 Rémy Sigrist, <a href="/A356245/a356245_2.png">Representation of the multiples of 5 in T(6)</a> %H A356245 Rémy Sigrist, <a href="/A356245/a356245.gp.txt">PARI program</a> %H A356245 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 A356245 Square A(0) is: %e A356245 1 1 %e A356245 1 1 %e A356245 Square A(1) is: %e A356245 1 2 2 1 %e A356245 2 3 3 2 %e A356245 2 3 3 2 %e A356245 1 2 2 1 %e A356245 Square A(2) is: %e A356245 1 3 3 2 4 4 2 3 3 1 %e A356245 3 5 6 5 7 7 5 6 5 3 %e A356245 3 6 7 5 8 8 5 7 6 3 %e A356245 2 5 5 3 6 6 3 5 5 2 %e A356245 4 7 8 6 9 9 6 8 7 4 %e A356245 4 7 8 6 9 9 6 8 7 4 %e A356245 2 5 5 3 6 6 3 5 5 2 %e A356245 3 6 7 5 8 8 5 7 6 3 %e A356245 3 5 6 5 7 7 5 6 5 3 %e A356245 1 3 3 2 4 4 2 3 3 1 %o A356245 (PARI) See Links section. %Y A356245 See A355855, A356002, A356096, A356097 and A356098 for similar sequences. %K A356245 nonn,tabf %O A356245 0,6 %A A356245 _Rémy Sigrist_, Jul 30 2022