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A162612 Triangle read by rows in which row n lists n terms, starting with n^2+n-1, with gaps = n^2-1 between successive terms.

%I A162612 #13 Mar 02 2024 13:49:03
%S A162612 1,5,8,11,19,27,19,34,49,64,29,53,77,101,125,41,76,111,146,181,216,55,
%T A162612 103,151,199,247,295,343,71,134,197,260,323,386,449,512,89,169,249,
%U A162612 329,409,489,569,649,729,109,208,307,406,505,604,703,802,901,1000,131,251
%N A162612 Triangle read by rows in which row n lists n terms, starting with n^2+n-1, with gaps = n^2-1 between successive terms.
%C A162612 Note that the last term of the n-th row is the n-th cube A000578(n).
%H A162612 Harvey P. Dale, <a href="/A162612/b162612.txt">Table of n, a(n) for n = 1..1000</a>
%F A162612 Sum_{k=1..n} T(n,k)= n*(n^3 + n^2 + n - 1)/2 (row sums). - _R. J. Mathar_, Jul 20 2009
%e A162612 Triangle begins:
%e A162612    1;
%e A162612    5,   8;
%e A162612   11,  19,  27;
%e A162612   19,  34,  49,  64;
%e A162612   29,  53,  77, 101, 125;
%e A162612   41,  76, 111, 146, 181, 216;
%t A162612 Table[NestList[#+n^2-1&,n^2+n-1,n-1],{n,20}]//Flatten (* _Harvey P. Dale_, Mar 02 2024 *)
%o A162612 (PARI) T(n,k)=n+k*(n^2-1) \\ _Franklin T. Adams-Watters_, Aug 06 2009
%Y A162612 Cf. A000578, A028387, A159797, A159798, A162610, A162611, A162613.
%K A162612 easy,nonn,tabl
%O A162612 1,2
%A A162612 _Omar E. Pol_, Jul 09 2009
%E A162612 More terms from _Franklin T. Adams-Watters_, Aug 06 2009