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A154614 Triangle read by rows where T(m,n) = m*n + m + n - 1, 1<=n<=m.

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%I A154614 #13 Sep 08 2022 08:45:40
%S A154614 2,4,7,6,10,14,8,13,18,23,10,16,22,28,34,12,19,26,33,40,47,14,22,30,
%T A154614 38,46,54,62,16,25,34,43,52,61,70,79,18,28,38,48,58,68,78,88,98,20,31,
%U A154614 42,53,64,75,86,97,108,119,22,34,46,58,70,82,94,106,118,130,142
%N A154614 Triangle read by rows where T(m,n) = m*n + m + n - 1, 1<=n<=m.
%C A154614 T(m,n)+2 = (n+1)*(m+1) is not prime.
%C A154614 T(m,m)+2 = (m+1)^2.
%C A154614 First column: A005843; second column: A112414; third column: 2*A020742; fourth column: A016885. - _Vincenzo Librandi_, Nov 17 2012
%H A154614 Vincenzo Librandi, <a href="/A154614/b154614.txt">Rows n = 1..100, flattened</a>
%e A154614 Triangle begins:
%e A154614 2;
%e A154614 4, 7;
%e A154614 6, 10, 14;
%e A154614 8, 13, 18, 23;
%e A154614 10, 16, 22, 28, 34;
%e A154614 12, 19, 26, 33, 40, 47;
%e A154614 14, 22, 30, 38, 46, 54, 62;
%e A154614 16, 25, 34, 43, 52, 61, 70, 79;
%e A154614 18, 28, 38, 48, 58, 68, 78, 88, 98;
%e A154614 20, 31, 42, 53, 64, 75, 86, 97, 108, 119; etc.
%t A154614 t[n_,k_]:=n*k + n + k - 1; Table[t[n, k], {n, 10}, {k, n}]//Flatten (* _Vincenzo Librandi_, Nov 17 2012 *)
%o A154614 (Magma) [(n*k + n + k - 1): k in [1..n], n in [1..11]]; // _Vincenzo Librandi_, Nov 17 2012
%Y A154614 Cf. A040976, A005843, A112414, A020742, A016885.
%K A154614 nonn,easy,tabl
%O A154614 1,1
%A A154614 _Vincenzo Librandi_, Jan 16 2009