A104572 Triangle read by rows: T(i,j) is the (i,j)-entry (1 <= j <= i) of the product A*B of the infinite lower triangular matrices A = [1; 3, 1; 5, 3, 1; 7, 5, 3, 1; ...] and B=[1; 2,1; 1,2,1; 2,1,2,1; ...].

1, 5, 1, 12, 5, 1, 22, 12, 5, 1, 35, 22, 12, 5, 1, 51, 35, 22, 12, 5, 1, 70, 51, 35, 22, 12, 5, 1, 92, 70, 51, 35, 22, 12, 5, 1, 117, 92, 70, 51, 35, 22, 12, 5, 1, 145, 117, 92, 70, 51, 35, 22, 12, 5, 1, 176, 145, 117, 92, 70, 51, 35, 22, 12, 5, 1, 210, 176, 145, 117, 92, 70, 51, 35

Offset

1,2

Links

Vincenzo Librandi, Rows n = 1..100, flattened

Formula

T(i,j) = (i-j+1)(3i-3j+2)/2 for 1 <= j <= i. - Emeric Deutsch, Mar 23 2005

Example

The first few rows are:
   1;
   5,  1;
  12,  5,  1;
  22, 12,  5,  1;
  35, 22, 12,  5,  1;
  ...

Maple

T:=proc(i, j) if j<=i then (i-j+1)*(3*i-3*j+2)/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

Mathematica

t[n_, k_]:=(n - k + 1) (3 n - 3 k + 2)/2; Table[t[n, k], {n, 11}, {k, n}]//Flatten (* Vincenzo Librandi, Aug 18 2017 *)

Prog

(Magma) /* As triangle */ [[(i-j+1)*(3*i-3*j+2)/2: j in [1..i]]: i in [1.. 7]]; // Vincenzo Librandi, Aug 18 2017

Crossrefs

Row sums yield the pentagonal pyramidal numbers (A002411). Columns (starting from the diagonal entries) are the pentagonal numbers (A000326).

Sequence in context: A347135 A146993 A343223 * A125232 A116923 A327797

Adjacent sequences: A104569 A104570 A104571 * A104573 A104574 A104575

Keyword

nonn,tabl

Author

Gary W. Adamson, Mar 16 2005

Extensions

More terms from Emeric Deutsch, Mar 23 2005

Status

approved