A162245 Triangle T(n,m) = 6*m*n + 3*m + 3*n + 1 read by rows.

13, 22, 37, 31, 52, 73, 40, 67, 94, 121, 49, 82, 115, 148, 181, 58, 97, 136, 175, 214, 253, 67, 112, 157, 202, 247, 292, 337, 76, 127, 178, 229, 280, 331, 382, 433, 85, 142, 199, 256, 313, 370, 427, 484, 541, 94, 157, 220, 283, 346, 409, 472, 535, 598, 661

Offset: 1

Author

Vincenzo Librandi, Jun 28 2009

Keywords

• nonn
• tabl
• easy

Comments

If h belongs to the main diagonal of the triangle then 6*h+3 is a square since T(n,n) = (3/2)*(2*n+1)^2-1/2 and 6*T(n,n)+3 = 9*(2*n+1)^2. Also, the first column is A017209 (after 4). - Vincenzo Librandi, Nov 20 2012

Examples

			Triangle begins:
13;
22, 37;
31, 52,  73;
40, 67,  94,  121;
49, 82,  115, 148, 181;
58, 97,  136, 175, 214, 253;
67, 112, 157, 202, 247, 292, 337;
76, 127, 178, 229, 280, 331, 382, 433; etc.
		

Links

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

Crossrefs

Cf. A003154, A017209, A083487, A163433.

Programs

Magma

[6*n*k + 3*n + 3*k + 1:  k in [1..n],  n in [1..11]]; // Vincenzo Librandi, Nov 20 2012

Mathematica

Flatten@Table[6*m*n + 3*m + 3*n + 1, {n, 20}, {m, n}] (* Vincenzo Librandi, Mar 03 2012 *)

Formula

Row sums: Sum_{m=1..n} T(n,m) = n*(5+6*n^2+15*n)/2. - R. J. Mathar, Jul 26 2009

T(n,m) = 3*A083487(n,m)+1. - R. J. Mathar, Jul 26 2009

T(k,k) = A003154(k+1) and T(k+1,k) = A163433(k+2). - Avi Friedlich, May 22 2015

Extensions

Edited by R. J. Mathar, Jul 26 2009