OFFSET
1,2
LINKS
Indranil Ghosh, Rows 1..100, flattened
Matthew Blair, Rigoberto Flórez, Antara Mukherjee, Matrices in the Hosoya triangle, arXiv:1808.05278 [math.CO], 2018.
H. Hosoya, Fibonacci Triangle, The Fibonacci Quarterly, 14;2, 1976, 173-178.
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.
Wikipedia, Hosoya triangle
FORMULA
T(n,k) = L(k)*L(n - k + 1), L(.) is a Lucas number.
EXAMPLE
Triangle begins:
1;
3, 3;
4, 9, 4;
7, 12, 12, 7;
11, 21, 16, 21, 11;
18, 33, 28, 28, 33, 18;
29, 54, 44, 49, 44, 54, 29;
...
MATHEMATICA
Table[LucasL[k] LucasL[n - k + 1] , {n, 10}, {k, n}] // Flatten (* Indranil Ghosh, Mar 31 2017 *)
PROG
(PARI) L(n) = fibonacci(n + 2) - fibonacci(n - 2);
for(n=1, 10, for(k=1, n, print1(L(k) * L(n - k + 1), ", "); ); print(); ) \\ Indranil Ghosh, Mar 31 2017
(Python)
from sympy import lucas
for n in range(1, 11):
....print [lucas(k) * lucas(n - k + 1) for k in range(1, n + 1)] # Indranil Ghosh, Mar 31 2017
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Rigoberto Florez, Mar 20 2017
STATUS
approved