A162624 Triangle read by rows in which row n lists n terms, starting with n^4 + n - 1, such that the difference between successive terms is equal to n^4 - 1 = A123865(n).

1, 17, 32, 83, 163, 243, 259, 514, 769, 1024, 629, 1253, 1877, 2501, 3125, 1301, 2596, 3891, 5186, 6481, 7776, 2407, 4807, 7207, 9607, 12007, 14407, 16807, 4103, 8198, 12293, 16388, 20483, 24578, 28673, 32768, 6569, 13129, 19689, 26249, 32809

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 5th power of n, A000584(n).

See also the triangles of A162622 and A162623.

Examples

			Triangle begins:
     1;
    17,   32;
    83,  163,  243;
   259,  514,  769, 1024;
   629, 1253, 1877, 2501, 3125;
  1301, 2596, 3891, 5186, 6481, 7776;
  ...
		

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000584, A123865, A159797, A162609, A162610, A162611, A162612, A162613, A162614, A162615, A162616, A162622, A162623.

Programs

Maple

A162624 := proc(n,k) return n+k*(n^4-1): end: seq(seq(A162624(n,k), k=1..n), n=1..10); # Nathaniel Johnston, Apr 30 2011

Mathematica

Table[NestList[#+n^4-1&,n^4+n-1,n-1],{n,10}]//Flatten (* Harvey P. Dale, Apr 28 2022 *)

Formula

Row sums: n*(n^5 + n^4 + n - 1)/2. - R. J. Mathar, Jul 20 2009