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A159798 Triangle read by rows in which row n lists n terms, starting with 1, such that the difference between successive terms is equal to n-3.

%I A159798 #10 Sep 08 2022 08:45:44
%S A159798 1,1,0,1,1,1,1,2,3,4,1,3,5,7,9,1,4,7,10,13,16,1,5,9,13,17,21,25,1,6,
%T A159798 11,16,21,26,31,36,1,7,13,19,25,31,37,43,49,1,8,15,22,29,36,43,50,57,
%U A159798 64,1,9,17,25,33,41,49,57,65,73,81,1,10,19,28,37,46,55,64,73,82,91,100,1,11
%N A159798 Triangle read by rows in which row n lists n terms, starting with 1, such that the difference between successive terms is equal to n-3.
%C A159798 Note that for n>1 the last term of the n-th row is the square A000290(n-2).
%C A159798 Row sums are n*(n^2-4*n+5)/2 = 1, 1, 3, 10, 25, 51, 91, 148, 225, ... - _R. J. Mathar_, Jul 17 2009, Jul 20 2009
%C A159798 Row sums are the positive terms of A162607. - _Omar E. Pol_, Jul 24 2009
%H A159798 G. C. Greubel, <a href="/A159798/b159798.txt">Table of n, a(n) for the first 100 rows, flattened</a>
%F A159798 T(n,k) = 1 + k*(n-3), 0<=k<n. - _R. J. Mathar_, Jul 17 2009
%e A159798 Triangle begins:
%e A159798   1;
%e A159798   1,  0;
%e A159798   1,  1,  1;
%e A159798   1,  2,  3,  4;
%e A159798   1,  3,  5,  7,  9;
%e A159798   1,  4,  7, 10, 13, 16;
%e A159798   1,  5,  9, 13, 17, 21, 25;
%e A159798   1,  6, 11, 16, 21, 26, 31, 36;
%e A159798   1,  7, 13, 19, 25, 31, 37, 43, 49;
%e A159798   1,  8, 15, 22, 29, 36, 43, 50, 57, 64;
%e A159798   1,  9, 17, 25, 33, 41, 49, 57, 65, 73, 81;
%e A159798   1, 10, 19, 28, 37, 46, 55, 64, 73, 82, 91, 100;
%t A159798 Table[1 + k*(n-3), {n, 1, 20}, {k, 0, n-1}]// Flatten (* _G. C. Greubel_, Apr 21 2018 *)
%o A159798 (PARI) for(n=1, 20, for(k=0,n-1, print1(1 + k*(n-3), ", "))) \\ _G. C. Greubel_, Apr 21 2018
%o A159798 (Magma) /* As triangle */ [[1 + k*(n-3): k in [0..n-1]]: n in [1..15]]; // _G. C. Greubel_, Apr 21 2018
%Y A159798 Cf. A000290, A081493, A159797, A162607, A162609, A162610, A162611.
%K A159798 easy,nonn,tabl
%O A159798 1,8
%A A159798 _Omar E. Pol_, Jul 09 2009
%E A159798 More terms from _R. J. Mathar_, Jul 17 2009
%E A159798 Typo in row sums corrected by _R. J. Mathar_, Jul 20 2009
%E A159798 Edited by _Omar E. Pol_, Jul 24 2009