A163676 Triangle T(n,m) = 4mn + 2m + 2n - 1 read by rows.

7, 13, 23, 19, 33, 47, 25, 43, 61, 79, 31, 53, 75, 97, 119, 37, 63, 89, 115, 141, 167, 43, 73, 103, 133, 163, 193, 223, 49, 83, 117, 151, 185, 219, 253, 287, 55, 93, 131, 169, 207, 245, 283, 321, 359, 61, 103, 145, 187, 229, 271, 313, 355, 397, 439, 67, 113, 159

Offset

1,1

Comments

2 + T(n,m) = (2*n+1)*(2*m+1) are composite numbers. - clarified by R. J. Mathar, Oct 16 2009

First column: A016921, second column: A017305, third column: A126980. - Vincenzo Librandi, Nov 21 2012

Links

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

Formula

T(n,m) = A155151(n,m) - 3 = A155156(n,m) - 1. - R. J. Mathar, Oct 16 2009

Example

Triangle begins:
   7;
  13,  23;
  19,  33,  47;
  25,  43,  61,  79;
  31,  53,  75,  97, 119;
  37,  63,  89, 115, 141, 167;
  43,  73, 103, 133, 163, 193, 223;
  49,  83, 117, 151, 185, 219, 253, 287;
  55,  93, 131, 169, 207, 245, 283, 321, 359;
  61, 103, 145, 187, 229, 271, 313, 355, 397, 439;

Mathematica

t[n_, k_]:=4 n*k + 2n + 2k - 1; Table[t[n, k], {n, 15}, {k, n}]//Flatten (* Vincenzo Librandi, Nov 21 2012 *)

Prog

(Magma) [4*n*k + 2*n + 2*k - 1: k in [1..n], n in [1..11]]; // Vincenzo Librandi, Nov 21 2012
(PARI) for(n=1, 10, for(k=1, n, print1(4*n*k + 2*n + 2*k - 1, ", "))) \\ G. C. Greubel, Aug 02 2017

Crossrefs

Cf. A016921, A017305, A126980, A155151, A155156.

Sequence in context: A034112 A236312 A301691 * A273605 A273641 A214794

Adjacent sequences: A163673 A163674 A163675 * A163677 A163678 A163679

Keyword

nonn,easy,tabl

Author

Vincenzo Librandi, Aug 03 2009

Status

approved