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A144712 Ordered sequence of Fibonomial coefficients. 3
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 (list; graph; refs; listen; history; text; internal format)
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, 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.

E. Lucas, Theorie des Fonctions Numeriques Simplement Periodiques, American J. Math. 1 (1878), 184-240, 289--321.

Edouard 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: A111501 A094565 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

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Last modified July 29 15:42 EDT 2021. Contains 346346 sequences. (Running on oeis4.)