A104583 Triangle read by rows: T(i,j) is the (i,j)-entry (1 <= j <= i) of the product A*B of the matrices A = [1; 3,1; 5,3,1; 7,5,3,1; ...]; B = [1; 1,2; 1,2,1; 1,2,1,2; ...] (both infinite lower triangular matrices).

1, 4, 2, 9, 8, 1, 16, 18, 4, 2, 25, 32, 9, 8, 1, 36, 50, 16, 18, 4, 2, 49, 72, 25, 32, 9, 8, 1, 64, 98, 36, 50, 16, 18, 4, 2, 81, 128, 49, 72, 25, 32, 9, 8, 1, 100, 162, 64, 98, 36, 50, 16, 18, 4, 2, 121, 200, 81, 128, 49, 72, 25, 32, 9, 8, 1, 144, 242, 100, 162, 64, 98, 36, 50, 16, 18

Offset

0,2

Links

Table of n, a(n) for n=0..75.

Formula

T(i, j) = (i-j+1)^2 if j <= i and j is odd; 2(i-j+1)^2 if j <= i and j is even; 0 if j > i. - Emeric Deutsch, Mar 23 2005

Example

The first few rows are:
   1;
   4,  2;
   9,  8,  1;
  16, 18,  4,  2;
  25, 32,  9,  8,  1;
  36, 50, 16, 18,  4,  2;
  49, 72, 25, 32,  9,  8,  1;
  ...

Maple

T:=proc(i, j) if j<=i and j mod 2=1 then (i-j+1)^2 elif j<=i and j mod 2 =0 then 2*(i-j+1)^2 else 0 fi end: for i from 1 to 13 do seq(T(i, j), j=1..i) od; # yields sequence in triangular form # Emeric Deutsch, Mar 23 2005

Crossrefs

Cf. A002411.

Row sums yield the pentagonal pyramidal numbers (A002411).

Sequence in context: A200639 A365255 A243968 * A278103 A249327 A182728

Adjacent sequences: A104580 A104581 A104582 * A104584 A104585 A104586

Keyword

nonn,tabl

Author

Gary W. Adamson, Mar 16 2005

Extensions

More terms from Emeric Deutsch, Mar 23 2005

Status

approved