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 A357990 #38 May 27 2024 23:15:12 %S A357990 1,1,1,3,1,1,1,5,1,1,7,1,7,1,1,3,19,1,9,1,1,7,5,37,1,11,1,1,1,11,7,61, %T A357990 1,13,1,1,15,1,15,9,91,1,15,1,1,7,65,1,19,11,127,1,17,1,1,17,19,175,1, %U A357990 23,13,169,1,19,1,1,3,43,37,369,1,27,15,217,1,21 %N A357990 Square array T(n, k), n >= 0, k > 0, read by antidiagonals, where T(0, k) = 1 for k > 0 and where T(n, k) = R(n, k+1) - R(n, k) for n > 0, k > 0. Here R(n, k) = T(A053645(n), k)*k^(A290255(n) + 1). %F A357990 Conjecture: T(n, 1) = A329369(n). %e A357990 Square array begins: %e A357990 1, 1, 1, 1, 1, 1, 1, 1, ... %e A357990 1, 1, 1, 1, 1, 1, 1, 1, ... %e A357990 3, 5, 7, 9, 11, 13, 15, 17, ... %e A357990 1, 1, 1, 1, 1, 1, 1, 1, ... %e A357990 7, 19, 37, 61, 91, 127, 169, 217, ... %e A357990 3, 5, 7, 9, 11, 13, 15, 17, ... %e A357990 7, 11, 15, 19, 23, 27, 31, 35, ... %e A357990 1, 1, 1, 1, 1, 1, 1, 1, ... %e A357990 15, 65, 175, 369, 671, 1105, 1695, 2465, ... %o A357990 (PARI) R(n,k)=my(L=logint(n, 2), A=n - 2^L); T(A, k)*k^(L - if(A>0, logint(A, 2) + 1) + 1) %o A357990 T(n,k)=if(n==0, 1, R(n, k+1) - R(n, k)) %o A357990 (PARI) T(n, k) = my(A = 2*n+1, B, C, v1, v2); v1 = []; while(A > 0, B=valuation(A, 2); v1=concat(v1, B+1); A \= 2^(B+1)); v1 = Vecrev(v1); A = #v1; v2 = vector(A, i, 1); for(i=1, A-1, B = A-i; for(j=1, B, C = B-j+k+1; v2[j] = v2[j]*C^v1[B] - v2[j+1]*(C-1)^v1[B])); v2[1] \\ _Mikhail Kurkov_, Apr 30 2024 %Y A357990 Cf. A000120, A053645, A290255, A329369. %K A357990 nonn,base,tabl %O A357990 0,4 %A A357990 _Mikhail Kurkov_, Nov 20 2022