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A162622 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.

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