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

Author

Gary W. Adamson, Mar 16 2005

Keywords

• nonn
• tabl

Comments

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

Examples

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

Links

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

Crossrefs

Cf. A001082, A006578, A104566, A104568.

Cf. A006578, A104566.

Programs

Maple

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

Mathematica

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

Formula

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

Extensions

More terms from Emeric Deutsch, Mar 24 2005