A163282 - OEIS

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

(list; table; graph; refs; listen; history; text; internal format)

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:

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