OFFSET
9,1
LINKS
R. Florez, R. Higuita and L. Junes, GCD property of the generalized star of David in the generalized Hosoya triangle, J. Integer Seq., 17 (2014), Article 14.3.6, 17 pp.
R. Florez and L. Junes, GCD properties in Hosoya's triangle, Fibonacci Quart. 50 (2012), 163-174.
H. Hosoya, Fibonacci Triangle, The Fibonacci Quarterly, 14;2, 1976, 173-178.
Wikipedia, Hosoya triangle
FORMULA
T(n,k) = (2^k + 1)*(2^(n - k + 1) + 1) n > 0, 0 < k <= n.
EXAMPLE
Triangle begins:
9;
15, 15;
27, 25, 27;
51, 45, 45, 51;
99, 85, 81, 85, 99;
195, 165, 153, 153, 165, 195;
...
MATHEMATICA
Table[(2^k + 1) (2^(n - k + 1) + 1), {n, 10}, {k, n}] // Flatten (* Indranil Ghosh, Apr 02 2017 *)
PROG
(PARI) T(n, k) = (2^k + 1)*(2^(n - k + 1) + 1);
tabl(nn) = for (n=1, nn, for (k=1, n, print1(T(n, k), ", ")); print()); \\ Michel Marcus, Apr 02 2017
(Python)
for n in range(1, 11):
....print [(2**k + 1) * (2**(n - k + 1) + 1) for k in range(1, n + 1)] # Indranil Ghosh, Apr 02 2017
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Rigoberto Florez, Mar 20 2017
STATUS
approved