A104568 Triangle of numbers that are 0 or 1 mod 3.

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, 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, 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

Offset: 0

Author

Gary W. Adamson, Mar 16 2005

Keywords

• nonn
• tabl

Comments

The matrix operations (J * R), (R * J) are commutative since J * R = R * J.

Row sums = A006578.

Rows and columns of the triangle are all 0 or 1 mod 3 terms: A032766.

A104567 row sums also = A006578.

A006578(2n-1) = A001082(2n).

Examples

			The first few rows are:
  1;
  3, 1;
  4, 3, 1;
  6, 4, 3, 1;
  7, 6, 4, 3, 1;
  9, 7, 6, 4, 3, 1;
  ...
		

Crossrefs

Cf. A001082, A006578, A104566, A104567.

Programs

Maple

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

Formula

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).

Extensions

More terms from James Sellers, Apr 09 2005