A155156 Triangle T(n, k) = 4*n*k + 2*n + 2*k, read by rows.

8, 14, 24, 20, 34, 48, 26, 44, 62, 80, 32, 54, 76, 98, 120, 38, 64, 90, 116, 142, 168, 44, 74, 104, 134, 164, 194, 224, 50, 84, 118, 152, 186, 220, 254, 288, 56, 94, 132, 170, 208, 246, 284, 322, 360, 62, 104, 146, 188, 230, 272, 314, 356, 398, 440, 68, 114, 160, 206, 252, 298, 344, 390, 436, 482, 528

Offset

1,1

Comments

First column: A016933, second column: A017317, third column: A063151, fourth column: 2*A017209. - Vincenzo Librandi, Nov 21 2012

Links

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

Formula

T(n, k) = 2*A083487(n, k). - R. J. Mathar, Jan 05 2011

Sum_{k=0..n} T(n,k) = n*(2*n^2 + 5*n + 1) = 2*A162254(n) = A163832(n). - G. C. Greubel, Mar 20 2021

Example

Triangle begins:
   8;
  14,  24;
  20,  34,  48;
  26,  44,  62,  80;
  32,  54,  76,  98, 120;
  38,  64,  90, 116, 142, 168;
  44,  74, 104, 134, 164, 194, 224;
  50,  84, 118, 152, 186, 220, 254, 288;
  56,  94, 132, 170, 208, 246, 284, 322, 360;
  62, 104, 146, 188, 230, 272, 314, 356, 398, 440;

Maple

seq(seq( 2*(2*n*k +n+k), k=1..n), n=1..15); # G. C. Greubel, Mar 20 2021

Mathematica

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

Prog

(Magma) [4*n*k + 2*n + 2*k : k in [1..n], n in [1..11]]; // Vincenzo Librandi, Nov 21 2012
(Sage) flatten([[2*(2*n*k +n+k) for k in (1..n)] for n in (1..15)]) # G. C. Greubel, Mar 20 2021

Crossrefs

Cf. A016933, A017317, A063151, A017209. A083487, A162254, A163832 (row sums).

Sequence in context: A053668 A218145 A250098 * A275898 A248427 A090993

Adjacent sequences: A155153 A155154 A155155 * A155157 A155158 A155159

Keyword

nonn,tabl,easy

Author

Vincenzo Librandi, Jan 21 2009

Extensions

Edited by Robert Hochberg, Jun 21 2010

Status

approved