A162622 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^4 - 1.

0, 1, 1, 2, 17, 32, 3, 83, 163, 243, 4, 259, 514, 769, 1024, 5, 629, 1253, 1877, 2501, 3125, 6, 1301, 2596, 3891, 5186, 6481, 7776, 7, 2407, 4807, 7207, 9607, 12007, 14407, 16807, 8, 4103, 8198, 12293, 16388, 20483, 24578, 28673, 32768, 9, 6569, 13129

Offset

0,4

Comments

Note that the last term of the n-th row is the 5th power of n, A000584(n).

See also the triangles of A162623 and A162624.

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Formula

Sum_{k=0..n} T(n,k) = n*(n+1)*(1+n^4)/2 (row sums). [R. J. Mathar, Jul 20 2009]

Example

Triangle begins:
  0;
  1,    1;
  2,   17,    32;
  3,   83,   163,   243;
  4,  259,   514,   769,  1024;
  5,  629,  1253,  1877,  2501,  3125;
  6, 1301,  2596,  3891,  5186,  6481,  7776;
  7, 2407,  4807,  7207,  9607, 12007, 14407, 16807;
  8, 4103,  8198, 12293, 16388, 20483, 24578, 28673, 32768;
  9, 6569, 13129, 19689, 26249, 32809, 39369, 45929, 52489, 59049; etc.

Maple

A162622 := proc(n, k) n+k*(n^4-1) ; end proc: seq(seq( A162622(n, k), k=0..n), n=0..15) ; # R. J. Mathar, Feb 11 2010

Mathematica

Flatten[Table[NestList[#+n^4-1&, n, n], {n, 0, 9}]] (* Harvey P. Dale, Jun 23 2013 *)

Prog

(Magma) /* Triangle: */ [[n+k*(n^4-1): k in [0..n]]: n in [0..10]]; // Bruno Berselli, Dec 14 2012

Crossrefs

Cf. A000583, A000584, A123865, A159797, A162609, A162610, A162611, A162612, A162613, A162614, A162615, A162616, A162623, A162624.

Sequence in context: A063118 A267540 A141068 * A078164 A060387 A003336

Adjacent sequences: A162619 A162620 A162621 * A162623 A162624 A162625

Keyword

nonn,easy,tabl

Author

Omar E. Pol, Jul 15 2009

Extensions

7th and later rows from R. J. Mathar, Feb 11 2010

Status

approved