A104566 Triangle read by rows: T(i,j) is the (i,j)-entry (1 <= j <= i) of the product H*R of the infinite lower triangular matrices H = [1; 1,2; 1,2,1; 1 2,1,2; ...] and R = [1; 1,1; 1,1,1; 1,1,1,1; ...].

1, 3, 2, 4, 3, 1, 6, 5, 3, 2, 7, 6, 4, 3, 1, 9, 8, 6, 5, 3, 2, 10, 9, 7, 6, 4, 3, 1, 12, 11, 9, 8, 6, 5, 3, 2, 13, 12, 10, 9, 7, 6, 4, 3, 1, 15, 14, 12, 11, 9, 8, 6, 5, 3, 2, 16, 15, 13, 12, 10, 9, 7, 6, 4, 3, 1, 18, 17, 15, 14, 12, 11, 9, 8, 6, 5, 3, 2, 19, 18, 16, 15, 13, 12, 10, 9, 7, 6, 4, 3, 1

Offset

1,2

Links

Table of n, a(n) for n=1..91.

Formula

For 1 <= j <= i: T(i,j) = 3(i-j+1)/2 if i and j are of opposite parity; T(i,j) = 3(i-j)/2 + 1 if both i and j are odd; T(i,j) = 3(i-j)/2 + 2 if both i and j are even. - Emeric Deutsch, Mar 24 2005

Example

The first few rows are
  1;
  3, 2;
  4, 3, 1;
  6, 5, 3, 2;
  ...

Maple

T:=proc(i, j) if j>i then 0 elif i mod 2 = 1 and j mod 2 = 1 then 3*(i-j)/2+1 elif i mod 2 = 0 and j mod 2 = 0 then 3*(i-j)/2+2 elif i+j mod 2 = 1 then 3*(i-j+1)/2 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

Crossrefs

Row sums yield A001082.

Columns 1, 3, 5, ... (starting at the diagonal entry) yield A032766.

Columns 2, 4, 6, ... (starting at the diagonal entry) yield A045506.

Row sums = 1, 5, 8, 16, 21, ... (generalized octagonal numbers, A001082). A006578(2n-1) = A001082(2n).

Sequence in context: A013633 A334662 A016559 * A143156 A227471 A101403

Adjacent sequences: A104563 A104564 A104565 * A104567 A104568 A104569

Keyword

nonn,tabl

Author

Gary W. Adamson, Mar 15 2005

Extensions

More terms from Emeric Deutsch, Mar 24 2005

Status

approved