A154614 - OEIS

%I #13 Sep 08 2022 08:45:40

%S 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 38,46,54,62,16,25,34,43,52,61,70,79,18,28,38,48,58,68,78,88,98,20,31,

%U 42,53,64,75,86,97,108,119,22,34,46,58,70,82,94,106,118,130,142

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

%C T(m,n)+2 = (n+1)*(m+1) is not prime.

%C T(m,m)+2 = (m+1)^2.

%C First column: A005843; second column: A112414; third column: 2*A020742; fourth column: A016885. - _Vincenzo Librandi_, Nov 17 2012

%H Vincenzo Librandi, <a href="/A154614/b154614.txt">Rows n = 1..100, flattened</a>

%e Triangle begins:

%e 2;

%e 4, 7;

%e 6, 10, 14;

%e 8, 13, 18, 23;

%e 10, 16, 22, 28, 34;

%e 12, 19, 26, 33, 40, 47;

%e 14, 22, 30, 38, 46, 54, 62;

%e 16, 25, 34, 43, 52, 61, 70, 79;

%e 18, 28, 38, 48, 58, 68, 78, 88, 98;

%e 20, 31, 42, 53, 64, 75, 86, 97, 108, 119; etc.

%t t[n_,k_]:=n*k + n + k - 1; Table[t[n, k], {n, 10}, {k, n}]//Flatten (* _Vincenzo Librandi_, Nov 17 2012 *)

%o (Magma) [(n*k + n + k - 1): k in [1..n], n in [1..11]]; // _Vincenzo Librandi_, Nov 17 2012

%Y Cf. A040976, A005843, A112414, A020742, A016885.

%K nonn,easy,tabl

%O 1,1

%A _Vincenzo Librandi_, Jan 16 2009