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Triangle T(n,m) = 2*m*n + m + n + 9 read by rows.
4

%I #14 Sep 08 2022 08:45:47

%S 13,16,21,19,26,33,22,31,40,49,25,36,47,58,69,28,41,54,67,80,93,31,46,

%T 61,76,91,106,121,34,51,68,85,102,119,136,153,37,56,75,94,113,132,151,

%U 170,189,40,61,82,103,124,145,166,187,208,229,43,66,89,112,135,158,181

%N Triangle T(n,m) = 2*m*n + m + n + 9 read by rows.

%C 2*T(m,n) - 17 =(2*n+1)*(2*m+1) and 2*T(n,n) - 17 is a square. Also:

%C first column: A112414;

%C second column: A016861;

%C third column: A017041;

%C fourth column: A017209. [_Vincenzo Librandi_, Nov 20 2012]

%H Vincenzo Librandi, <a href="/A163674/b163674.txt">Rows n = 1..100, flattened</a>

%F T(n,m) = A163657(n,m) + 1.

%e Triangle begins:

%e 13;

%e 16, 21;

%e 19, 26, 33;

%e 22, 31, 40, 49;

%e 25, 36, 47, 58, 69;

%e 28, 41, 54, 67, 80, 93;

%e 31, 46, 61, 76, 91, 106, 121;

%e 34, 51, 68, 85, 102, 119, 136, 153;

%t t[n_,k_]:=2 n*k + n + k + 9; Table[t[n, k], {n, 15}, {k, n}]//Flatten (* _Vincenzo Librandi_, Nov 20 2012 *)

%o (Magma) [2*n*k + n + k + 9: k in [1..n], n in [1..11]]; // _Vincenzo Librandi_, Nov 20 2012

%o (PARI) for(n=1,10, for(m=1,n, print1(2*m*n + m + n + 9, ", "))) \\ _G. C. Greubel_, Aug 02 2017

%Y Cf. A016861, A017041, A017209, A112414, A153051, A163657.

%K nonn,easy,tabl

%O 1,1

%A _Vincenzo Librandi_, Aug 03 2009

%E Edited by _R. J. Mathar_, Oct 12 2009