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Triangle read by rows: T(m,n) = 2mn + m + n - 4.
6

%I #26 Sep 08 2022 08:45:41

%S 0,3,8,6,13,20,9,18,27,36,12,23,34,45,56,15,28,41,54,67,80,18,33,48,

%T 63,78,93,108,21,38,55,72,89,106,123,140,24,43,62,81,100,119,138,157,

%U 176,27,48,69,90,111,132,153,174,195,216,30,53,76,99,122,145,168,191,214,237,260

%N Triangle read by rows: T(m,n) = 2mn + m + n - 4.

%C 2*T(m,n)+9 = (2m+1)*(2n+1). - _Vincenzo Librandi_, Nov 18 2012

%C First column: A008585; second column: A016885; third column: A017053; fourth column: 9*A020705. - _Vincenzo Librandi_, Nov 18 2012

%H Vincenzo Librandi, <a href="/A155724/b155724.txt">Rows n = 1..100, flattened</a>

%F T(m,n) = A154685(m,n) - 8. - _L. Edson Jeffery_, Oct 12 2012

%e Triangle begins:

%e 0;

%e 3, 8;

%e 6, 13, 20;

%e 9, 18, 27, 36;

%e 12, 23, 34, 45, 56;

%e 15, 28, 41, 54, 67, 80;

%e 18, 33, 48, 63, 78, 93, 108;

%e 21, 38, 55, 72, 89, 106, 123, 140;

%e 24, 43, 62, 81, 100, 119, 138, 157, 176;

%e 27, 48, 69, 90, 111, 132, 153, 174, 195, 216;

%t Flatten[Table[2 n m + m + n - 4, {n, 10}, {m, n}]] (* _Vincenzo Librandi_, Mar 01 2012 *)

%o (Magma) /* Triangle: */ [[2*m*n+m+n-4: m in [1..n]]: n in [1..10]]; // _Bruno Berselli_, Aug 31 2012

%Y All terms are in A155723.

%Y Cf. A154685, A155722, A162261 (row sums), A008585, A016885, A017053, A020705.

%K nonn,tabl,easy

%O 1,2

%A _Vincenzo Librandi_, Jan 25 2009

%E Edited by _N. J. A. Sloane_, Jun 23 2010