A284131 Hosoya triangle of Morgan Voyce type, read by rows.

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

Table of n, a(n) for n=1..48.

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

Adjacent sequences: A284128 A284129 A284130 * A284132 A284133 A284134

Keyword

nonn,tabl

Author

Rigoberto Florez, Mar 20 2017

Status

approved