login
A284131
Hosoya triangle of Morgan Voyce type, read by rows.
0
9, 21, 21, 54, 49, 54, 141, 126, 126, 141, 369, 329, 324, 329, 369, 966, 861, 846, 846, 861, 966, 2529, 2254, 2214, 2209, 2214, 2254, 2529, 6621, 5901, 5796, 5781, 5781, 5796, 5901, 6621, 17334, 15449, 15174, 15134, 15129, 15134, 15174, 15449, 17334, 45381, 40446, 45381
OFFSET
1,1
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.
Eric Weisstein's World of Mathematics, Morgan-Voyce polynomials
Wikipedia, Hosoya Triangle
FORMULA
T(n,k) = L(2k)L(2(n - k + 1)), L(.) is a Lucas number; 0 < n, 0 < k <= n.
EXAMPLE
Triangle begins:
9;
21, 21;
54, 49, 54;
141, 126, 126, 141;
369, 329, 324, 329, 369;
...
MATHEMATICA
Table[LucasL[2k] LucasL[2(n - k + 1)], {n, 10}, {k, n}] // Flatten (* Indranil Ghosh, Mar 30 2017 *)
PROG
(PARI) L(n) = fibonacci(n + 2) - fibonacci(n - 2);
for(n=1, 10, for(k=1, n, print1(L(2*k)*L(2*(n - k + 1)), ", "); ); print(); ); \\ Indranil Ghosh, Mar 30 2017
(Python)
from sympy import lucas
for n in range(1, 11):
....print [lucas(2*k) * lucas(2*(n - k + 1)) for k in range(1, n + 1)] # Indranil Ghosh, Mar 30 2017
CROSSREFS
Cf. A000032.
Sequence in context: A250783 A259250 A251219 * A111171 A317789 A333039
KEYWORD
nonn,tabl
AUTHOR
Rigoberto Florez, Mar 20 2017
STATUS
approved