cp's OEIS Frontend

A162614 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^3 - 1.

%I A162614 #17 May 08 2025 19:41:28
%S A162614 0,1,1,2,9,16,3,29,55,81,4,67,130,193,256,5,129,253,377,501,625,6,221,
%T A162614 436,651,866,1081,1296,7,349,691,1033,1375,1717,2059,2401,8,519,1030,
%U A162614 1541,2052,2563,3074,3585,4096,9,737,1465,2193,2921,3649,4377,5105,5833
%N A162614 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^3 - 1.
%C A162614 Note that the last term of the n-th row is the fourth power of n, A000583(n).
%C A162614 See also the triangles of A162615 and A162616.
%F A162614 Sum_{k=0..n} T(n,k) = n*(n^2-n+1)*(n+1)^2/2 (row sums). - _R. J. Mathar_, Jul 20 2009
%F A162614 T(n,k) = n + k*(n^3-1). - _R. J. Mathar_, Oct 20 2009
%e A162614 Triangle begins:
%e A162614   0;
%e A162614   1,   1;
%e A162614   2,   9,  16;
%e A162614   3,  29,  55,  81;
%e A162614   4,  67, 130, 193, 256;
%e A162614   5, 129, 253, 377, 501,  625;
%e A162614   6, 221, 436, 651, 866, 1081, 1296;
%e A162614   ...
%o A162614 (Python)
%o A162614 def A162614(n,k):
%o A162614     return n+k*(n**3-1)
%o A162614 print([A162614(n,k) for n in range(20) for k in range(n+1)])
%o A162614 # _R. J. Mathar_, Oct 20 2009
%Y A162614 Cf. A000583, A068601, A159797, A162609, A162610, A162611, A162612, A162613, A162615, A162616, A162622, A162623, A162624.
%K A162614 easy,nonn,tabl
%O A162614 0,4
%A A162614 _Omar E. Pol_, Jul 15 2009
%E A162614 More terms from _R. J. Mathar_, Oct 20 2009