%I #36 Dec 07 2019 12:18:28

%S 9,15,15,27,25,27,51,45,45,51,99,85,81,85,99,195,165,153,153,165,195,

%T 387,325,297,289,297,325,387,771,645,585,561,561,585,645,771,1539,

%U 1285,1161,1105,1089,1105,1161,1285,1539,3075,2565,2313,2193,2145,2145,2193,2313,2565,3075

%N Hosoya triangle of Fermat Lucas type, read by rows.

%H R. Florez, R. Higuita and L. Junes, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL17/Florez/florez3.html">GCD property of the generalized star of David in the generalized Hosoya triangle</a>, J. Integer Seq., 17 (2014), Article 14.3.6, 17 pp.

%H R. Florez and L. Junes, <a href="http://leandrojunes.com/wp-content/uploads/2014/07/FlorezJunes.pdf">GCD properties in Hosoya's triangle</a>, Fibonacci Quart. 50 (2012), 163-174.

%H H. Hosoya, <a href="http://www.fq.math.ca/Scanned/14-2/hosoya.pdf">Fibonacci Triangle</a>, The Fibonacci Quarterly, 14;2, 1976, 173-178.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Hosoya%27s_triangle">Hosoya triangle</a>

%F T(n,k) = (2^k + 1)*(2^(n - k + 1) + 1) n > 0, 0 < k <= n.

%e Triangle begins:

%e 9;

%e 15, 15;

%e 27, 25, 27;

%e 51, 45, 45, 51;

%e 99, 85, 81, 85, 99;

%e 195, 165, 153, 153, 165, 195;

%e ...

%t Table[(2^k + 1) (2^(n - k + 1) + 1), {n, 10}, {k, n}] // Flatten (* _Indranil Ghosh_, Apr 02 2017 *)

%o (PARI) T(n,k) = (2^k + 1)*(2^(n - k + 1) + 1);

%o tabl(nn) = for (n=1, nn, for (k=1, n, print1(T(n,k), ", ")); print()); \\ _Michel Marcus_, Apr 02 2017

%o (Python)

%o for n in range(1, 11):

%o ....print [(2**k + 1) * (2**(n - k + 1) + 1) for k in range(1, n + 1)] # _Indranil Ghosh_, Apr 02 2017

%K nonn,tabl

%O 9,1

%A _Rigoberto Florez_, Mar 20 2017