A284115 Hosoya triangle of Lucas type.

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, 47, 87, 72, 77, 77, 72, 87, 47, 76, 141, 116, 126, 121, 126, 116, 141, 76, 123, 228, 188, 203, 198, 198, 203, 188, 228, 123, 199, 369, 304, 329, 319, 324, 319, 329, 304, 369, 199

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

Cf. A000032.

Sequence in context: A197431 A197672 A348884 * A183501 A086239 A016605

Adjacent sequences: A284112 A284113 A284114 * A284116 A284117 A284118

Keyword

nonn,tabl,changed

Author

Rigoberto Florez, Mar 20 2017

Status

approved