A162614 -id:A162614 - cp's OEIS frontend

A163283 Triangle read by rows in which row n lists n+1 terms, starting with n^3 and ending with n^4, such that the difference between successive terms is equal to n^3 - n^2.

0, 1, 1, 8, 12, 16, 27, 45, 63, 81, 64, 112, 160, 208, 256, 125, 225, 325, 425, 525, 625, 216, 396, 576, 756, 936, 1116, 1296, 343, 637, 931, 1225, 1519, 1813, 2107, 2401, 512, 960, 1408, 1856, 2304, 2752, 3200, 3648, 4096, 729, 1377, 2025, 2673, 3321, 3969

Offset: 0

Omar E. Pol, Jul 24 2009

The first term of row n is A000578(n) and the last term of row n is A000583(n).

			Triangle begins:
0;
1,    1;
8,    12,   16;
27,   45,   63,   81;
64,   112,  160,  208,  256;
125,  225,  325,  425,  525,  625;
216,  396,  576,  756,  936,  1116, 1296;
343,  637,  931,  1225, 1519, 1813, 2107, 2401;
512,  960,  1408, 1856, 2304, 2752, 3200, 3648, 4096;
729,  1377, 2025, 2673, 3321, 3969, 4617, 5265, 5913, 6561;
1000, 1900, 2800, 3700, 4600, 5500, 6400, 7300, 8200, 9100, 10000;
...

G. C. Greubel, Table of n, a(n) for the first 50 rows

Row sums: A099903.

Cf. A000578, A000583, A045991, A159797, A162611, A162614, A163282, A163284, A163285.

Table[n^3 + k*(n^3 - n^2), {n, 0, 5}, {k, 0, n}]//Flatten (* G. C. Greubel, Dec 13 2016 *)

A163283(n, k)=n^3 +k*(n^3 -n^2) \\ G. C. Greubel, Dec 13 2016

T(n, k) = n^3 + k*(n^3 - n^2), for 0 <= k <= n, n >= 0. - G. C. Greubel, Dec 13 2016

Edited by Omar E. Pol, Jul 25 2009

A162618 Triangle read by rows in which row n lists n consecutive natural numbers A000027, starting with A008578(n-1) - n + 1.

Original entry on oeis.org

1, 1, 2, 1, 2, 3, 2, 3, 4, 5, 3, 4, 5, 6, 7, 6, 7, 8, 9, 10, 11, 7, 8, 9, 10, 11, 12, 13, 10, 11, 12, 13, 14, 15, 16, 17, 11, 12, 13, 14, 15, 16, 17, 18, 19, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30

Offset: 1

Omar E. Pol, Jul 10 2009

Note that the last term of the n-th row is the noncomposite number A008578(n-1).

			Contribution from _Omar E. Pol_, Jul 15 2009: (Start)
Triangle begins:
   1;
   1,  2;
   1,  2,  3;
   2,  3,  4,  5;
   3,  4,  5,  6,  7;
   6,  7,  8,  9, 10, 11;
   7,  8,  9, 10, 11, 12, 13;
  10, 11, 12, 13, 14, 15, 16, 17;
  11, 12, 13, 14, 15, 16, 17, 18, 19;
  14, 15, 16, 17, 18, 19, 20, 21, 22, 23;
  19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29;
  20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31;
(End)

Cf. A000040, A008578, A159797, A159798, A162611, A162619, A162620.

Cf. A162614, A162622. - Omar E. Pol, Jul 15 2009

cp's OEIS Frontend

A163283 Triangle read by rows in which row n lists n+1 terms, starting with n^3 and ending with n^4, such that the difference between successive terms is equal to n^3 - n^2.

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