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 A332963 #24 Mar 18 2020 04:17:47 %S A332963 1,2,2,1,5,1,2,3,3,2,1,7,2,7,1,2,4,5,5,4,2,1,9,3,13,3,9,1,2,5,7,8,8,7, %T A332963 5,2,1,11,4,19,5,19,4,11,1,2,6,9,11,12,12,11,9,6,2,1,13,5,25,7,29,7, %U A332963 25,5,13,1,2,7,11,14,16,17,17,16,14,11,7,2 %N A332963 Number triangle where T(2n,0)=T(2n,2n)=1, T(2n+1,0)=T(2n+1,2n+1)=2 for all n >= 0, and the interior numbers are defined recursively by T(n,k) = (T(n-1,k-1)*T(n-1,k)+1)/T(n-2,k-1) for n > 2, 0 < k <= n. %H A332963 Philip K. Hotchkiss, <a href="https://arxiv.org/abs/1907.11159">Generalized Rascal Triangles</a>, arXiv:1907.11159 [math.HO], 2019, Figure 10 p. 4. %F A332963 By rows: a(2n,0)=a(2n,2n)=1, a(2n+1,0)=a(2n+1,2n+1)=2 for all n >= 0, while the interior numbers are defined recursively by a(n,k) = (a(n-1,k-1)*a(n-1,k)+1)/a(n-2,k-1) for n >= 2, 0 < k <= n. %F A332963 By antidiagonals: T(0,2n)=T(2n,0)=1, T(0,2n+1)=T(2n+1,0)=2 for all n >= 0, while the interior numbers are defined recursively by T(r,k) = (T(r-1,k)*(Tr,k-1)+1)/T(r-1,k-1) for r,k > 0. %e A332963 For row 3: a(3,0)=2, a(3,1)= 3, a(3,2)=3, a(3,3)=2. %e A332963 For antidiagonal 3: T(3,0)=2, T(3,1)=7, T(3,2)=5, T(3,3)=13, ... %e A332963 Triangle begins: %e A332963 1; %e A332963 2, 2; %e A332963 1, 5, 1; %e A332963 2, 3, 3, 2; %e A332963 1, 7, 2, 7, 1; %e A332963 2, 4, 5, 5, 4, 2; %e A332963 ... %o A332963 (PARI) T(n, k) = if ((n<0) || (n<k), 0, if ((k==0) || (k==n), if (n%2, 2, 1), (T(n-1,k-1)*T(n-1,k)+1)/T(n-2,k-1))); %o A332963 matrix(7, 7, n, k, T(n-1,k-1)) \\ to see the triangle \\ _Michel Marcus_, Mar 16 2020 %Y A332963 Cf. A077028, A309555, A309557, A332790, A309559 %K A332963 nonn,tabl %O A332963 0,2 %A A332963 _Philip K Hotchkiss_, Mar 04 2020