A163652 Triangle read by rows where T(n,m)=2*m*n + m + n + 6.

10, 13, 18, 16, 23, 30, 19, 28, 37, 46, 22, 33, 44, 55, 66, 25, 38, 51, 64, 77, 90, 28, 43, 58, 73, 88, 103, 118, 31, 48, 65, 82, 99, 116, 133, 150, 34, 53, 72, 91, 110, 129, 148, 167, 186, 37, 58, 79, 100, 121, 142, 163, 184, 205, 226, 40, 63, 86, 109, 132, 155, 178

Offset: 1

Author

Vincenzo Librandi, Aug 02 2009

Keywords

• nonn
• easy
• tabl

Comments

The numbers 2*T(n,m)-11 = (2*n+1)*(2*m+1) are not prime, and 2*T(n,n) = (2n+1)^2.

First column: A112414, second column: A016885, third column: A017005, fourth column: A017173. - Vincenzo Librandi, Nov 20 2012

Examples

			Triangle begins:
  10;
  13, 18;
  16, 23, 30;
  19, 28, 37, 46;
  22, 33, 44, 55,  66;
  25, 38, 51, 64,  77,  90;
  28, 43, 58, 73,  88,  103, 118;
  31, 48, 65, 82,  99,  116, 133, 150;
  34, 53, 72, 91,  110, 129, 148, 167, 186;
  37, 58, 79, 100, 121, 142, 163, 184, 205, 226;
  40, 63, 86, 109, 132, 155, 178, 201, 224, 247, 270;
  etc.
		

Links

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

Crossrefs

Cf. A153045, A154685, A163657, A112414, A016885, A017005, A017173.

Programs

Magma

[2*n*k + n + k + 6: k in [1..n], n in [1..11]]; // Vincenzo Librandi, Nov 20 2012

Mathematica

t[n_,k_]:=2 n*k + n + k +  6; Table[t[n, k], {n, 15}, {k, n}]//Flatten (* Vincenzo Librandi, Nov 20 2012 *)

Formula

T(n,m) = A154685(n,m)+2 = A163657(n,m)-2. [R. J. Mathar, Oct 22 2009]

Extensions

Comment clarified by R. J. Mathar, Oct 22 2009