A163282 Triangle read by rows in which row n lists n+1 terms, starting with n^2 and ending with n^3, such that difference between successive terms is equal to n^2 - n.

0, 1, 1, 4, 6, 8, 9, 15, 21, 27, 16, 28, 40, 52, 64, 25, 45, 65, 85, 105, 125, 36, 66, 96, 126, 156, 186, 216, 49, 91, 133, 175, 217, 259, 301, 343, 64, 120, 176, 232, 288, 344, 400, 456, 512, 81, 153, 225, 297, 369, 441, 513, 585, 657, 729, 100, 190, 280, 370, 460, 550

Offset

0,4

Comments

The first term of row n is A000290(n) and the last term of row n is A000578(n).

Links

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

Formula

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

Example

Triangle begins:
    0;
    1,   1;
    4,   6,   8;
    9,  15,  21,  27;
   16,  28,  40,  52,  64;
   25,  45,  65,  85, 105, 125;
   36,  66,  96, 126, 156, 186, 216;
   49,  91, 133, 175, 217, 259, 301, 343;
   64, 120, 176, 232, 288, 344, 400, 456, 512;
   81, 153, 225, 297, 369, 441, 513, 585, 657, 729;
  100, 190, 280, 370, 460, 550, 640, 730, 820, 910, 1000;

Mathematica

T[n_, k_] := n^2 + k*(n^2 - n); Table[T[n, k], {n, 0, 10}, {k, 0, n}] //Flatten (* G. C. Greubel, Dec 13 2016 *)
Join[{0, 1}, Table[Range[n^2, n^3, n^2-n], {n, 10}]]//Flatten (* Harvey P. Dale, Sep 09 2019 *)

Prog

(PARI) A163282(n, k)=n^2+k*(n^2-n) \\ Michael B. Porter, Feb 25 2010
(Magma) /* As triangle: */ [[n^2+k*(n^2-n): k in [0..n]]: n in [0.. 15]]; // Vincenzo Librandi, Dec 13 2016

Crossrefs

Cf. A000290, A000578, A002378, A159797, A162611, A163283, A163284, A163285.

Sequence in context: A275624 A228019 A228020 * A095404 A073540 A123710

Adjacent sequences: A163279 A163280 A163281 * A163283 A163284 A163285

Keyword

nonn,tabl,easy

Author

Omar E. Pol, Jul 24 2009

Status

approved