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

Author

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

Keywords

• nonn

Comments

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

Examples

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

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.

Crossrefs

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

Programs

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 *)

Formula

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

Extensions

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