A162615 Triangle read by rows in which row n lists n terms, starting with n, such that the difference between successive terms is equal to n^3 - 1 = A068601(n).

1, 2, 9, 3, 29, 55, 4, 67, 130, 193, 5, 129, 253, 377, 501, 6, 221, 436, 651, 866, 1081, 7, 349, 691, 1033, 1375, 1717, 2059, 8, 519, 1030, 1541, 2052, 2563, 3074, 3585, 9, 737, 1465, 2193, 2921, 3649, 4377, 5105, 5833, 10, 1009, 2008, 3007, 4006, 5005, 6004

Offset: 1

Author

Omar E. Pol, Jul 12 2009

Keywords

• easy
• nonn
• tabl

Comments

See also the triangles of A162614 and A162616.

Examples

			Triangle begins:
  1;
  2,   9;
  3,  29,  55;
  4,  67, 130, 193;
  5, 129, 253, 377, 501;
  6, 221, 436, 651, 866, 1081;
  ...
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000583, A068601, A159797, A162609, A162610, A162611, A162612, A162613, A162614, A162616.

Programs

Maple

A162615 := proc(n,k) n+(k-1)*(n^3-1) ; end proc: seq(seq(A162615(n,k),k=1..n),n=1..15) ; # R. J. Mathar, Feb 05 2010

Mathematica

Flatten[Table[c=n^3-1;NestList[#+c&,n,n-1],{n,10}]] (* Harvey P. Dale, Nov 13 2011 *)

Formula

Row sums: n*(n^4 - n^3 + n + 1)/2. - R. J. Mathar, Jul 20 2009

Extensions

Terms beyond the 6th row from R. J. Mathar and Max Alekseyev, Feb 05 2010