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

0,2

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).

Links

Table of n, a(n) for n=0..90.

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).

Example

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;
  ...

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 A. Sellers, Apr 09 2005

Crossrefs

Cf. A001082, A006578, A104566, A104567.

Sequence in context: A064883 A090844 A008314 * A030758 A347065 A322103

Adjacent sequences: A104565 A104566 A104567 * A104569 A104570 A104571

Keyword

nonn,tabl

Author

Gary W. Adamson, Mar 16 2005

Extensions

More terms from James A. Sellers, Apr 09 2005

Status

approved