A162616 Triangle read by rows in which row n lists n terms, starting with n^3 + n - 1, such that the difference between successive terms is equal to n^3 - 1 = A068601(n).

1, 9, 16, 29, 55, 81, 67, 130, 193, 256, 129, 253, 377, 501, 625, 221, 436, 651, 866, 1081, 1296, 349, 691, 1033, 1375, 1717, 2059, 2401, 519, 1030, 1541, 2052, 2563, 3074, 3585, 4096, 737, 1465, 2193, 2921, 3649, 4377, 5105, 5833, 6561, 1009, 2008

Offset: 1

Author

Omar E. Pol, Jul 12 2009

Keywords

• easy
• nonn
• tabl

Comments

Note that the last term of the n-th row is the fourth power of n, A000583(n).

See also the triangles of A162614 and A162615.

Examples

			Triangle begins:
    1;
    9,  16;
   29,  55,  81;
   67, 130, 193, 256;
  129, 253, 377, 501,  625;
  221, 436, 651, 866, 1081, 1296;
  ...
		

Links

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

Crossrefs

Cf. A000583, A068601, A159797, A162609, A162610, A162611, A162612, A162613, A162614, A162615.

Programs

Maple

A162616 := proc(n,k) n^3+n-1+(k-1)*(n^3-1) ; end proc: seq(seq(A162616(n,k),k=1..n),n=1..15) ; # R. J. Mathar, Feb 05 2010

Mathematica

Table[NestList[#+n^3-1&,n^3+n-1,n-1],{n,10}]//Flatten (* Harvey P. Dale, Dec 17 2021 *)

Formula

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

Extensions

More terms from R. J. Mathar, Feb 05 2010