A163674 Triangle T(n,m) = 2*m*n + m + n + 9 read by rows.

13, 16, 21, 19, 26, 33, 22, 31, 40, 49, 25, 36, 47, 58, 69, 28, 41, 54, 67, 80, 93, 31, 46, 61, 76, 91, 106, 121, 34, 51, 68, 85, 102, 119, 136, 153, 37, 56, 75, 94, 113, 132, 151, 170, 189, 40, 61, 82, 103, 124, 145, 166, 187, 208, 229, 43, 66, 89, 112, 135, 158, 181

Offset: 1

Author

Vincenzo Librandi, Aug 03 2009

Keywords

• nonn
• easy
• tabl

Comments

2*T(m,n) - 17 =(2*n+1)*(2*m+1) and 2*T(n,n) - 17 is a square. Also:

first column: A112414;

second column: A016861;

third column: A017041;

fourth column: A017209. [Vincenzo Librandi, Nov 20 2012]

Examples

			Triangle begins:
  13;
  16,  21;
  19,  26,  33;
  22,  31,  40,  49;
  25,  36,  47,  58,  69;
  28,  41,  54,  67,  80,  93;
  31,  46,  61,  76,  91, 106, 121;
  34,  51,  68,  85, 102, 119, 136, 153;
		

Links

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

Crossrefs

Cf. A016861, A017041, A017209, A112414, A153051, A163657.

Programs

Magma

[2*n*k + n + k + 9: k in [1..n], n in [1..11]]; // Vincenzo Librandi, Nov 20 2012

Mathematica

t[n_,k_]:=2 n*k + n + k + 9; Table[t[n, k], {n, 15}, {k, n}]//Flatten (* Vincenzo Librandi, Nov 20 2012 *)

PARI

for(n=1,10, for(m=1,n, print1(2*m*n + m + n + 9, ", "))) \\ G. C. Greubel, Aug 02 2017

Formula

T(n,m) = A163657(n,m) + 1.

Extensions

Edited by R. J. Mathar, Oct 12 2009