A162612 Triangle read by rows in which row n lists n terms, starting with n^2+n-1, with gaps = n^2-1 between successive terms.

1, 5, 8, 11, 19, 27, 19, 34, 49, 64, 29, 53, 77, 101, 125, 41, 76, 111, 146, 181, 216, 55, 103, 151, 199, 247, 295, 343, 71, 134, 197, 260, 323, 386, 449, 512, 89, 169, 249, 329, 409, 489, 569, 649, 729, 109, 208, 307, 406, 505, 604, 703, 802, 901, 1000, 131, 251

Offset

1,2

Comments

Note that the last term of the n-th row is the n-th cube A000578(n).

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

Sum_{k=1..n} T(n,k)= n*(n^3 + n^2 + n - 1)/2 (row sums). - R. J. Mathar, Jul 20 2009

Example

Triangle begins:
   1;
   5,   8;
  11,  19,  27;
  19,  34,  49,  64;
  29,  53,  77, 101, 125;
  41,  76, 111, 146, 181, 216;

Mathematica

Table[NestList[#+n^2-1&, n^2+n-1, n-1], {n, 20}]//Flatten (* Harvey P. Dale, Mar 02 2024 *)

Prog

(PARI) T(n, k)=n+k*(n^2-1) \\ Franklin T. Adams-Watters, Aug 06 2009

Crossrefs

Cf. A000578, A028387, A159797, A159798, A162610, A162611, A162613.

Sequence in context: A314399 A175319 A154486 * A314400 A314401 A355168

Adjacent sequences: A162609 A162610 A162611 * A162613 A162614 A162615

Keyword

easy,nonn,tabl

Author

Omar E. Pol, Jul 09 2009

Extensions

More terms from Franklin T. Adams-Watters, Aug 06 2009

Status

approved