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 A155151 Triangle read by rows: T(m, n) = 4mn + 2m + 2n + 2, where m is the row and n is the position in the row, for 1 <= n <= m. 3

%I

%S 10,16,26,22,36,50,28,46,64,82,34,56,78,100,122,40,66,92,118,144,170,

%T 46,76,106,136,166,196,226,52,86,120,154,188,222,256,290,58,96,134,

%U 172,210,248,286,324,362,64,106,148,190,232,274,316,358,400,442,70,116,162

%N Triangle read by rows: T(m, n) = 4mn + 2m + 2n + 2, where m is the row and n is the position in the row, for 1 <= n <= m.

%C First column: A016957, second column: A017341, third column: 2*A017029, fourth column: A082286. - _Vincenzo Librandi_, Nov 21 2012

%C Conjecture: Let p = prime number. If 2^p belongs to T(m, n) = 4*m*n + 2*m + 2*n + 2, then 2^p-1 is not a Mersenne prime. - _Vincenzo Librandi_, Dec 12 2012

%H Vincenzo Librandi, <a href="/A155151/b155151.txt">Rows n = 1..100, flattened</a>

%F T(m,n) = 2*A144650(m,n).

%e 10;

%e 16, 26;

%e 22, 36, 50;

%e 28, 46, 64, 82;

%e 34, 56, 78, 100, 122;

%e 40, 66, 92, 118, 144, 170;

%e 46, 76, 106, 136, 166, 196, 226;

%e 52, 86, 120, 154, 188, 222, 256, 290;

%e 58, 96, 134, 172, 210, 248, 286, 324, 362;

%e 64, 106, 148, 190, 232, 274, 316, 358, 400, 442; etc.

%t t[n_,k_]:=4 n*k + 2n + 2k + 2; Table[t[n, k], {n, 11}, {k, n}]//Flatten (* _Vincenzo Librandi_, Nov 21 2012 *)

%o (MAGMA) [4*n*k + 2*n + 2*k + 2: k in [1..n], n in [1..11]]; // _Vincenzo Librandi_, Nov 21 2012

%Y Cf. A000668, A144650, A016957, A017341, A017029, A082286.

%K nonn,tabl,easy

%O 1,1

%A _Vincenzo Librandi_, Jan 21 2009

%E Edited by Robert Hochberg, Jun 21 2010

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