A143254 Triangle read by rows, T(n,k) = (4n-3)*(4k-3); 1<=k<=n.

1, 5, 25, 9, 45, 81, 13, 65, 117, 169, 17, 85, 153, 221, 289, 21, 105, 189, 273, 357, 441, 25, 125, 225, 325, 425, 525, 625, 29, 145, 261, 377, 493, 609, 725, 841, 33, 165, 297, 429, 561, 693, 825, 957, 1089, 37, 185, 333, 481, 629, 777, 925, 1073, 1221, 1369

Offset: 1

Author

Gary W. Adamson, Aug 02 2008

Keywords

• nonn
• tabl

Comments

Row sums = A100147: (1, 30, 135, 364, 765,...).

Examples

			First few rows of the triangle =
1;
5, 25;
9, 45, 81;
13, 65, 117, 169;
17, 85, 153, 221, 289;
21, 105, 189, 273, 357, 441;
...
T(5,3) = 153 = (4n-3)*(4k-3) = 17*9
		

Links

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

Crossrefs

Cf. A016813, A100147.

Programs

Mathematica

Flatten[Table[(4 n - 3) (4 k - 3), {n, 10}, {k, n}]] (* Harvey P. Dale, Feb 28 2015 *)

Formula

Triangle read by rows, T(n,k) = (4n-3)*(4k-3); 1<=k<=n, where (4k-3) = A016813: (1, 5, 9, 13, 17,...). Let X = an infinite lower triangular matrix with (1, 5, 9, 13,...) in the main diagonal and the rest zeros. The triangle = X * A000012 * X, where A000012 = an infinite lower triangular matrix with all 1's: (1; 1,1; 1,1,1;...)