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

1,1

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]

Links

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

Formula

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

Example

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;

Mathematica

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

Prog

(Magma) [2*n*k + n + k + 9: k in [1..n], n in [1..11]]; // 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

Crossrefs

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

Sequence in context: A159975 A350300 A110623 * A280062 A132947 A205876

Adjacent sequences: A163671 A163672 A163673 * A163675 A163676 A163677

Keyword

nonn,easy,tabl

Author

Vincenzo Librandi, Aug 03 2009

Extensions

Edited by R. J. Mathar, Oct 12 2009

Status

approved