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A154684 Triangle read by rows where T(m,n)=2mn + m + n - 3, 1<=n<=m.

%I A154684 #11 Sep 08 2022 08:45:40
%S A154684 1,4,9,7,14,21,10,19,28,37,13,24,35,46,57,16,29,42,55,68,81,19,34,49,
%T A154684 64,79,94,109,22,39,56,73,90,107,124,141,25,44,63,82,101,120,139,158,
%U A154684 177,28,49,70,91,112,133,154,175,196,217,31,54,77,100,123,146,169
%N A154684 Triangle read by rows where T(m,n)=2mn + m + n - 3, 1<=n<=m.
%C A154684 2*T(m,n)+7 = (2n+1)*(2m+1) is not prime.
%C A154684 First column: A016777; second column: A016897; third column: A008589; fourth column: A017173. - _Vincenzo Librandi_, Nov 19 2012
%H A154684 Vincenzo Librandi, <a href="/A154684/b154684.txt">Rows n = 1..100, flattened</a>
%e A154684 Triangle begins:
%e A154684 1;
%e A154684 4,  9;
%e A154684 7,  14, 21;
%e A154684 10, 19, 28, 37;
%e A154684 13, 24, 35, 46, 57;
%e A154684 16, 29, 42, 55, 68,  81;
%e A154684 19, 34, 49, 64, 79,  94,  109;
%e A154684 22, 39, 56, 73, 90,  107, 124, 141;
%e A154684 25, 44, 63, 82, 101, 120, 139, 158, 177;
%e A154684 28, 49, 70, 91, 112, 133, 154, 175, 196, 217; etc.
%t A154684 t[n_,k_]:=2 n*k + n + k - 3; Table[t[n, k], {n, 20}, {k, n}]//Flatten (* _Vincenzo Librandi_, Nov 19 2012 *)
%o A154684 (Magma) [(2*n*k + n + k - 3): k in [1..n], n in [1..11]]; // _Vincenzo Librandi_, Nov 19 2012
%Y A154684 Cf. A153053, A105760, A162265 (row sums), A016777, A016897, A008589, A017173.
%K A154684 nonn,tabl,easy
%O A154684 1,2
%A A154684 _Vincenzo Librandi_, Jan 18 2009