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 A144083 #27 Feb 26 2023 19:35:20 %S A144083 1,2,1,2,2,1,1,2,2,1,0,1,2,2,1,0,0,1,2,2,1,1,0,0,1,2,2,1,2,1,0,0,1,2, %T A144083 2,1,2,2,1,0,0,1,2,2,1,1,2,2,1,0,0,1,2,2,1,0,1,2,2,1,0,0,1,2,2,1,0,0, %U A144083 1,2,2,1,0,0,1,2,2,1 %N A144083 Triangle read by rows: partial sums from the right of an A010892 subsequences decrescendo triangle. %C A144083 n-th row = (n+1) terms of an infinitely periodic cycle: (..., 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1), shifting to the right one place for the next row. %C A144083 Construct an A010892 decrescendo triangle: (1; 1,1; 0,1,1; -1,0,1,1; ...) and take partial sums starting from the right. %F A144083 T(n, k) = 1 + A010892(n-k-1), with 0 <= k <= n. - _Stefano Spezia_, Feb 11 2023 %e A144083 First few rows of the triangle: %e A144083 1; %e A144083 2, 1; %e A144083 2, 2, 1; %e A144083 1, 2, 2, 1; %e A144083 0, 1, 2, 2, 1; %e A144083 0, 0, 1, 2, 2, 1; %e A144083 1, 0, 0, 1, 2, 2, 1; %e A144083 2, 1, 0, 0, 1, 2, 2, 1; %e A144083 2, 2, 1, 0, 0, 1, 2, 2, 1; %e A144083 1, 2, 2, 1, 0, 0, 1, 2, 2, 1; %e A144083 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1; %e A144083 ... %e A144083 Row 3 = (1, 2, 2, 1) = partial sums of (-1, 0, 1, 1). %t A144083 A010892[n_]:={1, 1, 0, -1, -1,0}[[Mod[n, 6]+1]]; T[n_,k_]:=1+A010892[n-k-1]; Table[T[n,k], {n,0, 11},{k,0,n}]//Flatten (* _Stefano Spezia_, Feb 11 2023 *) %Y A144083 Cf. A010892, A077859 (row sums), A164965 (1st column). %K A144083 nonn,tabl %O A144083 0,2 %A A144083 _Gary W. Adamson_, Sep 10 2008