A284128 Hosoya triangle of Fermat Lucas type, read by rows.

9, 15, 15, 27, 25, 27, 51, 45, 45, 51, 99, 85, 81, 85, 99, 195, 165, 153, 153, 165, 195, 387, 325, 297, 289, 297, 325, 387, 771, 645, 585, 561, 561, 585, 645, 771, 1539, 1285, 1161, 1105, 1089, 1105, 1161, 1285, 1539, 3075, 2565, 2313, 2193, 2145, 2145, 2193, 2313, 2565, 3075

Offset

9,1

Links

Table of n, a(n) for n=9..63.

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

Sequence in context: A346609 A232395 A184048 * A058957 A257409 A105882

Adjacent sequences: A284125 A284126 A284127 * A284129 A284130 A284131

Keyword

nonn,tabl

Author

Rigoberto Florez, Mar 20 2017

Status

approved