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A104568 Triangle of numbers that are 0 or 1 mod 3. 1
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 (list; table; graph; refs; listen; history; text; internal format)
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 A322103 A272172

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

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Last modified April 6 19:34 EDT 2020. Contains 333286 sequences. (Running on oeis4.)