A162614 Triangle read by rows in which row n lists n+1 terms, starting with n, such that the difference between successive terms is equal to n^3 - 1.

0, 1, 1, 2, 9, 16, 3, 29, 55, 81, 4, 67, 130, 193, 256, 5, 129, 253, 377, 501, 625, 6, 221, 436, 651, 866, 1081, 1296, 7, 349, 691, 1033, 1375, 1717, 2059, 2401, 8, 519, 1030, 1541, 2052, 2563, 3074, 3585, 4096, 9, 737, 1465, 2193, 2921, 3649, 4377, 5105, 5833

Offset

0,4

Comments

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

See also the triangles of A162615 and A162616.

Links

Table of n, a(n) for n=0..53.

Formula

Sum_{k=0..n} T(n,k) = n*(n^2-n+1)*(n+1)^2/2 (row sums). - R. J. Mathar, Jul 20 2009

T(n,k) = n + k*(n^3-1). - R. J. Mathar, Oct 20 2009

Example

Triangle begins:
  0;
  1,   1;
  2,   9,  16;
  3,  29,  55,  81;
  4,  67, 130, 193, 256;
  5, 129, 253, 377, 501,  625;
  6, 221, 436, 651, 866, 1081, 1296;
  ...

Prog

From R. J. Mathar, Oct 20 2009: (Start)
(Python)
def A162614(n, k):
    return n+k*(n**3-1)
print([A162614(n, k) for n in range(20) for k in range(n+1)])
(End)

Crossrefs

Cf. A000583, A068601, A159797, A162609, A162610, A162611, A162612, A162613, A162615, A162616, A162622, A162623, A162624.

Sequence in context: A067547 A166374 A083783 * A031238 A224859 A136345

Adjacent sequences: A162611 A162612 A162613 * A162615 A162616 A162617

Keyword

easy,nonn,tabl

Author

Omar E. Pol, Jul 15 2009

Extensions

More terms from R. J. Mathar, Oct 20 2009

Status

approved