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

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, 41, 48, 56, 12, 21, 29, 38, 46, 55, 63, 72, 14, 23, 33, 42, 52, 61, 71, 80, 90, 15, 26, 36, 47, 57, 68, 78, 89, 99, 110, 17, 28, 40, 51, 63, 74, 86, 97, 109, 120, 132, 18, 31, 43, 56, 68

Offset

1,1

Comments

From Vincenzo Librandi, Nov 16 2012: (Start)

First column: A007494(n+1);

second column: A047219(n+2);

third column: A047383(n+3);

fourth column: A193910(n+4).

Conjecture: If h does not belong to the sequence, then 4*h+1 is prime. (End)

Links

Vincenzo Librandi, Rows n = 1..100, flattened

Example

Triangle begins:
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, 41, 48, 56; etc.

Mathematica

Flatten[Table[Floor[(2*n*m + m + n)/2], {n, 1, 20}, {m, n}]] (* Vincenzo Librandi, Nov 16 2012 *)

Prog

(Magma) [Floor((2*n*k+n+k)/2): k in [1..n], n in [1..11]]; // Vincenzo Librandi, Nov 16 2012

Crossrefs

Cf. A007494, A047219, A047383, A193910.

Sequence in context: A276081 A329564 A257011 * A035493 A363277 A070038

Adjacent sequences: A144649 A144650 A144651 * A144653 A144654 A144655

Keyword

nonn,tabl,easy

Author

Vincenzo Librandi, Jan 27 2009

Extensions

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

Status

approved