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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 (list; table; graph; refs; listen; history; text; internal format)
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)^2-1/2 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

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Last modified November 28 22:51 EST 2022. Contains 358421 sequences. (Running on oeis4.)