A144712 Ordered sequence of Fibonomial coefficients.

1, 2, 3, 5, 6, 8, 13, 15, 21, 34, 40, 55, 60, 89, 104, 144, 233, 260, 273, 377, 610, 714, 987, 1092, 1597, 1820, 1870, 2584, 4181, 4641, 4895, 6765, 10946, 12376, 12816, 17711, 19635, 28657, 33552, 46368, 75025, 83215, 85085, 87841, 121393, 136136

Offset

1,2

Comments

All Fibonacci numbers are present except 0. Members which are not Fibonacci numbers: A171159. (* Robert G. Wilson v, Dec 04 2009 *)

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..88

D. E. Knuth and H. S. Wilf, The Power of a Prime that Divides a Generalized Binomial Coefficient, J. Reine Angew. Math. 396 (1989), 212-219.

Édouard Lucas, Théorie des Fonctions Numériques Simplement Périodiques, American J. Math. 1 (1878), 184-240, 289--321.

Édouard Lucas, The Theory of Simply Periodic Numerical Functions, Fibonacci Association, 1969. English translation of article "Théorie des Fonctions Numériques Simplement Périodiques, I", Amer. J. Math., 1 (1878), 184-240.

Diego Marques and Pavel Trojovsky, On Divisibility of Fibonomial Coefficients by 3, Journal of Integer Sequences, Vol. 15 (2012), #12.6.4.

Formula

{[n,k]_F = (F_n...F_{n-k+1})/(F_1...F_k),n,k integers} = {f_1 < f_2 < f_3 < ...}

Example

f_1=1, f_2=2, f_3=3, f_4=5, f_5=6.

Mathematica

f[n_, k_] := Product[Fibonacci[n - j + 1]/Fibonacci[j], {j, k}]; Take[ Union@ Flatten@ Table[ f[n, i], {n, 0, 27}, {i, 0, n}], 47] (* Robert G. Wilson v, Dec 04 2009 *)

Crossrefs

Cf. A010048. - Robert G. Wilson v, Dec 04 2009

Sequence in context: A094565 A364122 A034722 * A050028 A239135 A179791

Adjacent sequences: A144709 A144710 A144711 * A144713 A144714 A144715

Keyword

nonn

Author

Florian Luca and Pante Stanica (pstanica(AT)nps.edu), Sep 19 2008

Extensions

a(16)-a(47) from Robert G. Wilson v, Dec 04 2009

Status

approved