

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
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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(2n1) = 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



