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%I #15 Sep 08 2022 08:45:46
%S 0,1,1,4,6,8,9,15,21,27,16,28,40,52,64,25,45,65,85,105,125,36,66,96,
%T 126,156,186,216,49,91,133,175,217,259,301,343,64,120,176,232,288,344,
%U 400,456,512,81,153,225,297,369,441,513,585,657,729,100,190,280,370,460,550
%N 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.
%C The first term of row n is A000290(n) and the last term of row n is A000578(n).
%H G. C. Greubel, <a href="/A163282/b163282.txt">Table of n, a(n) for the first 50 rows</a>
%F T(n, k) = n^2 + k*(n^2 - n), for 0 <= k <= n, n>= 0. - _G. C. Greubel_, Dec 13 2016
%e Triangle begins:
%e 0;
%e 1, 1;
%e 4, 6, 8;
%e 9, 15, 21, 27;
%e 16, 28, 40, 52, 64;
%e 25, 45, 65, 85, 105, 125;
%e 36, 66, 96, 126, 156, 186, 216;
%e 49, 91, 133, 175, 217, 259, 301, 343;
%e 64, 120, 176, 232, 288, 344, 400, 456, 512;
%e 81, 153, 225, 297, 369, 441, 513, 585, 657, 729;
%e 100, 190, 280, 370, 460, 550, 640, 730, 820, 910, 1000;
%t 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 *)
%t Join[{0,1},Table[Range[n^2,n^3,n^2-n],{n,10}]]//Flatten (* _Harvey P. Dale_, Sep 09 2019 *)
%o (PARI) A163282(n,k)=n^2+k*(n^2-n) \\ _Michael B. Porter_, Feb 25 2010
%o (Magma) /* As triangle: */ [[n^2+k*(n^2-n): k in [0..n]]: n in [0.. 15]]; // _Vincenzo Librandi_, Dec 13 2016
%Y Cf. A000290, A000578, A002378, A159797, A162611, A163283, A163284, A163285.
%K nonn,tabl,easy
%O 0,4
%A _Omar E. Pol_, Jul 24 2009
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