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A162245 Triangle T(n,m) = 6*m*n + 3*m + 3*n + 1 read by rows.

%I A162245 #37 Sep 08 2022 08:45:46
%S A162245 13,22,37,31,52,73,40,67,94,121,49,82,115,148,181,58,97,136,175,214,
%T A162245 253,67,112,157,202,247,292,337,76,127,178,229,280,331,382,433,85,142,
%U A162245 199,256,313,370,427,484,541,94,157,220,283,346,409,472,535,598,661
%N A162245 Triangle T(n,m) = 6*m*n + 3*m + 3*n + 1 read by rows.
%C A162245 If h belongs to the main diagonal of the triangle then 6*h+3 is a square since T(n,n) = (3/2)*(2*n+1)^2-1/2 and 6*T(n,n)+3 = 9*(2*n+1)^2. Also, the first column is A017209 (after 4). - _Vincenzo Librandi_, Nov 20 2012
%H A162245 Vincenzo Librandi, <a href="/A162245/b162245.txt">Rows n = 1..100, flattened</a>
%F A162245 Row sums: Sum_{m=1..n} T(n,m) = n*(5+6*n^2+15*n)/2. - _R. J. Mathar_, Jul 26 2009
%F A162245 T(n,m) = 3*A083487(n,m)+1. - _R. J. Mathar_, Jul 26 2009
%F A162245 T(k,k) = A003154(k+1) and T(k+1,k) = A163433(k+2). - _Avi Friedlich_, May 22 2015
%e A162245 Triangle begins:
%e A162245 13;
%e A162245 22, 37;
%e A162245 31, 52,  73;
%e A162245 40, 67,  94,  121;
%e A162245 49, 82,  115, 148, 181;
%e A162245 58, 97,  136, 175, 214, 253;
%e A162245 67, 112, 157, 202, 247, 292, 337;
%e A162245 76, 127, 178, 229, 280, 331, 382, 433; etc.
%t A162245 Flatten@Table[6*m*n + 3*m + 3*n + 1, {n, 20}, {m, n}] (* _Vincenzo Librandi_, Mar 03 2012 *)
%o A162245 (Magma) [6*n*k + 3*n + 3*k + 1:  k in [1..n],  n in [1..11]]; // _Vincenzo Librandi_, Nov 20 2012
%Y A162245 Cf. A003154, A017209, A083487, A163433.
%K A162245 nonn,tabl,easy
%O A162245 1,1
%A A162245 _Vincenzo Librandi_, Jun 28 2009
%E A162245 Edited by _R. J. Mathar_, Jul 26 2009