

A162245


Triangle T(n,m) = 6*m*n + 3*m + 3*n + 1 read by rows.


2



13, 22, 37, 31, 52, 73, 40, 67, 94, 121, 49, 82, 115, 148, 181, 58, 97, 136, 175, 214, 253, 67, 112, 157, 202, 247, 292, 337, 76, 127, 178, 229, 280, 331, 382, 433, 85, 142, 199, 256, 313, 370, 427, 484, 541, 94, 157, 220, 283, 346, 409, 472, 535, 598, 661
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OFFSET

1,1


COMMENTS

If h belongs to the main diagonal of the triangle then 6*h+3 is a square since T(n,n) = (3/2)*(2*n+1)^21/2 and 6*T(n,n)+3 = 9*(2*n+1)^2. Also, the first column is A017209 (after 4).  Vincenzo Librandi, Nov 20 2012


LINKS

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


FORMULA

Row sums: Sum_{m=1..n} T(n,m) = n*(5+6*n^2+15*n)/2.  R. J. Mathar, Jul 26 2009
T(n,m) = 3*A083487(n,m)+1.  R. J. Mathar, Jul 26 2009
T(k,k) = A003154(k+1) and T(k+1,k) = A163433(k+2).  Avi Friedlich, May 22 2015


EXAMPLE

Triangle begins:
13;
22, 37;
31, 52, 73;
40, 67, 94, 121;
49, 82, 115, 148, 181;
58, 97, 136, 175, 214, 253;
67, 112, 157, 202, 247, 292, 337;
76, 127, 178, 229, 280, 331, 382, 433; etc.


MATHEMATICA

Flatten@Table[6*m*n + 3*m + 3*n + 1, {n, 20}, {m, n}] (* Vincenzo Librandi, Mar 03 2012 *)


PROG

(Magma) [6*n*k + 3*n + 3*k + 1: k in [1..n], n in [1..11]]; // Vincenzo Librandi, Nov 20 2012


CROSSREFS

Cf. A003154, A017209, A083487, A163433.
Sequence in context: A059408 A164455 A164504 * A159302 A172187 A164412
Adjacent sequences: A162242 A162243 A162244 * A162246 A162247 A162248


KEYWORD

nonn,tabl,easy


AUTHOR

Vincenzo Librandi, Jun 28 2009


EXTENSIONS

Edited by R. J. Mathar, Jul 26 2009


STATUS

approved



