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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.
5

%I #11 Dec 14 2016 20:12:19

%S 0,1,1,8,12,16,27,45,63,81,64,112,160,208,256,125,225,325,425,525,625,

%T 216,396,576,756,936,1116,1296,343,637,931,1225,1519,1813,2107,2401,

%U 512,960,1408,1856,2304,2752,3200,3648,4096,729,1377,2025,2673,3321,3969

%N 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.

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

%H G. C. Greubel, <a href="/A163283/b163283.txt">Table of n, a(n) for the first 50 rows</a>

%F T(n, k) = n^3 + k*(n^3 - n^2), for 0 <= k <= n, n >= 0. - _G. C. Greubel_, Dec 13 2016

%e Triangle begins:

%e 0;

%e 1, 1;

%e 8, 12, 16;

%e 27, 45, 63, 81;

%e 64, 112, 160, 208, 256;

%e 125, 225, 325, 425, 525, 625;

%e 216, 396, 576, 756, 936, 1116, 1296;

%e 343, 637, 931, 1225, 1519, 1813, 2107, 2401;

%e 512, 960, 1408, 1856, 2304, 2752, 3200, 3648, 4096;

%e 729, 1377, 2025, 2673, 3321, 3969, 4617, 5265, 5913, 6561;

%e 1000, 1900, 2800, 3700, 4600, 5500, 6400, 7300, 8200, 9100, 10000;

%e ...

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

%o (PARI) A163283(n, k)=n^3 +k*(n^3 -n^2) \\ _G. C. Greubel_, Dec 13 2016

%Y Row sums: A099903.

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

%K easy,nonn,tabl

%O 0,4

%A _Omar E. Pol_, Jul 24 2009

%E Edited by _Omar E. Pol_, Jul 25 2009