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A144652 Triangle, read by rows, where T(m,n) = floor((2mn+m+n)/2) with m >= n >= 1.

%I A144652 #22 Sep 08 2022 08:45:38
%S A144652 2,3,6,5,8,12,6,11,15,20,8,13,19,24,30,9,16,22,29,35,42,11,18,26,33,
%T A144652 41,48,56,12,21,29,38,46,55,63,72,14,23,33,42,52,61,71,80,90,15,26,36,
%U A144652 47,57,68,78,89,99,110,17,28,40,51,63,74,86,97,109,120,132,18,31,43,56,68
%N A144652 Triangle, read by rows, where T(m,n) = floor((2mn+m+n)/2) with m >= n >= 1.
%C A144652 From _Vincenzo Librandi_, Nov 16 2012: (Start)
%C A144652 First column:  A007494(n+1);
%C A144652 second column: A047219(n+2);
%C A144652 third column:  A047383(n+3);
%C A144652 fourth column: A193910(n+4).
%C A144652 Conjecture: If h does not belong to the sequence, then 4*h+1 is prime. (End)
%H A144652 Vincenzo Librandi, <a href="/A144652/b144652.txt">Rows n = 1..100, flattened</a>
%e A144652 Triangle begins:
%e A144652 2;
%e A144652 3,  6;
%e A144652 5,  8,  12;
%e A144652 6,  11, 15, 20;
%e A144652 8,  13, 19, 24, 30;
%e A144652 9,  16, 22, 29, 35, 42;
%e A144652 11, 18, 26, 33, 41, 48, 56; etc.
%t A144652 Flatten[Table[Floor[(2*n*m + m + n)/2], {n, 1, 20}, {m, n}]] (* _Vincenzo Librandi_, Nov 16 2012 *)
%o A144652 (Magma) [Floor((2*n*k+n+k)/2): k in [1..n], n in [1..11]]; // _Vincenzo Librandi_, Nov 16 2012
%Y A144652 Cf. A007494, A047219, A047383, A193910.
%K A144652 nonn,tabl,easy
%O A144652 1,1
%A A144652 _Vincenzo Librandi_, Jan 27 2009
%E A144652 Definition edited (specifying m >= n >= 1), and terms recomputed to match definition, as was done with the similar sequence A140869, by _Jon E. Schoenfield_, Jun 24 2010