A104566 -id:A104566 - cp's OEIS frontend

A104567 Triangle read by rows: T(i,j) = i-j+1 if j is odd; T(i,j) = 2(i-j+1) if j is even (1 <= j <= i).

1, 2, 2, 3, 4, 1, 4, 6, 2, 2, 5, 8, 3, 4, 1, 6, 10, 4, 6, 2, 2, 7, 12, 5, 8, 3, 4, 1, 8, 14, 6, 10, 4, 6, 2, 2, 9, 16, 7, 12, 5, 8, 3, 4, 1, 10, 18, 8, 14, 6, 10, 4, 6, 2, 2, 11, 20, 9, 16, 7, 12, 5, 8, 3, 4, 1, 12, 22, 10, 18, 8, 14, 6, 10, 4, 6, 2, 2, 13, 24, 11, 20, 9, 16, 7, 12, 5, 8, 3, 4, 1, 14

Offset: 1

Gary W. Adamson, Mar 16 2005

T(i,j) is the (i,j)-entry (1<=j<=i) of the product R*H of the infinite lower triangular matrices R = [1; 1,1; 1,1,1; 1,1,1,1; ...] and H = [1; 1,2; 1,2,1; 1 2,1,2; ...]. Row sums yield A006578. H*R yields A104566. - Emeric Deutsch, Mar 24 2005

			The first few rows are:
  1;
  2, 2;
  3, 4, 1;
  4, 6, 2, 2;

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A001082, A006578, A104566, A104568.

Cf. A006578, A104566.

T:=proc(i,j) if j>i then 0 elif j mod 2 = 1 then i-j+1 elif j mod 2 = 0 then 2*(i-j+1) else fi end: for i from 1 to 14 do seq(T(i,j),j=1..i) od; # yields sequence in triangular form # Emeric Deutsch, Mar 24 2005

Table[If[OddQ[j],i-j+1,2(i-j+1)],{i,20},{j,i}]//Flatten (* Harvey P. Dale, Sep 03 2018 *)

T(i,j) = i-j+1 if j is odd; T(i,j) = 2(i-j+1) if j is even (1 <= j <= i). - Emeric Deutsch, Mar 24 2005

More terms from Emeric Deutsch, Mar 24 2005

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

Original entry on oeis.org

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

Gary W. Adamson, Mar 16 2005

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).

			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;
  ...

Cf. A001082, A006578, A104566, A104567.

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

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).

More terms from James Sellers, Apr 09 2005

cp's OEIS Frontend

A104567 Triangle read by rows: T(i,j) = i-j+1 if j is odd; T(i,j) = 2(i-j+1) if j is even (1 <= j <= i).

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