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%I #14 Sep 08 2022 08:45:46
%S 0,1,1,2,17,32,3,83,163,243,4,259,514,769,1024,5,629,1253,1877,2501,
%T 3125,6,1301,2596,3891,5186,6481,7776,7,2407,4807,7207,9607,12007,
%U 14407,16807,8,4103,8198,12293,16388,20483,24578,28673,32768,9,6569,13129
%N Triangle read by rows in which row n lists n+1 terms, starting with n, such that the difference between successive terms is equal to n^4 - 1.
%C Note that the last term of the n-th row is the 5th power of n, A000584(n).
%C See also the triangles of A162623 and A162624.
%H Harvey P. Dale, <a href="/A162622/b162622.txt">Table of n, a(n) for n = 0..1000</a>
%F Sum_{k=0..n} T(n,k) = n*(n+1)*(1+n^4)/2 (row sums). [_R. J. Mathar_, Jul 20 2009]
%e Triangle begins:
%e 0;
%e 1, 1;
%e 2, 17, 32;
%e 3, 83, 163, 243;
%e 4, 259, 514, 769, 1024;
%e 5, 629, 1253, 1877, 2501, 3125;
%e 6, 1301, 2596, 3891, 5186, 6481, 7776;
%e 7, 2407, 4807, 7207, 9607, 12007, 14407, 16807;
%e 8, 4103, 8198, 12293, 16388, 20483, 24578, 28673, 32768;
%e 9, 6569, 13129, 19689, 26249, 32809, 39369, 45929, 52489, 59049; etc.
%p A162622 := proc(n,k) n+k*(n^4-1) ; end proc: seq(seq( A162622(n,k),k=0..n),n=0..15) ; # _R. J. Mathar_, Feb 11 2010
%t Flatten[Table[NestList[#+n^4-1&,n,n],{n,0,9}]] (* _Harvey P. Dale_, Jun 23 2013 *)
%o (Magma) /* Triangle: */ [[n+k*(n^4-1): k in [0..n]]: n in [0..10]]; // _Bruno Berselli_, Dec 14 2012
%Y Cf. A000583, A000584, A123865, A159797, A162609, A162610, A162611, A162612, A162613, A162614, A162615, A162616, A162623, A162624.
%K nonn,easy,tabl
%O 0,4
%A _Omar E. Pol_, Jul 15 2009
%E 7th and later rows from _R. J. Mathar_, Feb 11 2010
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