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 A104568 #11 Jul 02 2025 16:02:02 %S A104568 1,3,1,4,3,1,6,4,3,1,7,6,4,3,1,9,7,6,4,3,1,10,9,7,6,4,3,1,12,10,9,7,6, %T A104568 4,3,1,13,12,10,9,7,6,4,3,1,15,13,12,10,9,7,6,4,3,1,16,15,13,12,10,9, %U A104568 7,6,4,3,1,18,16,15,13,12,10,9,7,6,4,3,1,19,18,16,15,13,12,10,9,7,6,4,3,1 %N A104568 Triangle of numbers that are 0 or 1 mod 3. %C A104568 The matrix operations (J * R), (R * J) are commutative since J * R = R * J. %C A104568 Row sums = A006578. %C A104568 Rows and columns of the triangle are all 0 or 1 mod 3 terms: A032766. %C A104568 A104567 row sums also = A006578. %C A104568 A006578(2n-1) = A001082(2n). %F A104568 All columns (with offset); and all rows (starting from the right) are 0 or 1 mod 3 (A032766). Extract the triangle from the product J * R; J = [1; 2, 1; 1, 2, 1; 2, 1, 2, 1; ...]; R = [1; 1, 1; 1, 1, 1; ...] (infinite lower triangular matrices, with the rest zeros). %e A104568 The first few rows are: %e A104568 1; %e A104568 3, 1; %e A104568 4, 3, 1; %e A104568 6, 4, 3, 1; %e A104568 7, 6, 4, 3, 1; %e A104568 9, 7, 6, 4, 3, 1; %e A104568 ... %p A104568 it:=array(1..1000): i:=1: for n from 1 to 1000 do if n mod 3 <> 2 then it[i]:=n; i:=i+1 fi: od: for j from 1 to 25 do for k from j to 1 by -1 do printf(`%d,`,it[k]) od: od: # _James Sellers_, Apr 09 2005 %Y A104568 Cf. A001082, A006578, A104566, A104567. %K A104568 nonn,tabl %O A104568 0,2 %A A104568 _Gary W. Adamson_, Mar 16 2005 %E A104568 More terms from _James Sellers_, Apr 09 2005