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Search: id:A144712
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| A144712 |
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Ordered sequence of Fibonomial coefficients |
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+0
3
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| 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; listen)
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OFFSET
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1,2
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COMMENT
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All Fibonacci numbers are present except 0. Members which are not Fibonacci numbers: 6, 15, 40, 60, 104, 260, 273, 714, 1092, 1820, 1870, 4641, 4895, 12376, ..., . [From Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 04 2009]
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REFERENCES
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E. Lucas, Theorie des Fonctions Numeriques Simplement Periodiques, American J. Math. 1 (1878), 184--240, 289--321.
D. E. Knuth and H. S. Wilf, The Power of a Prime that Divides a Generalized Binomial Coefficient, J. Reine Angev. Math. 396 (1989), 212--219.
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FORMULA
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{[n,k]_F=(F_n...F_{n-k+1})/(F_1...F_k),n,k integers}={f_1<f_2<f_3<...}
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EXAMPLE
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f_1=1,f_2=2,f_3=3,f_4=5,f_5=6
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MATHEMATICA
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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] [From Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 04 2009]
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CROSSREFS
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Sequence in context: A111501 A094565 A034722 this_sequence A050028 A139443 A088497
Adjacent sequences: A144709 A144710 A144711 this_sequence A144713 A144714 A144715
Cf. A010048. [From Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 04 2009]
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KEYWORD
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nonn,new
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AUTHOR
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Florian Luca and Pante Stanica (pstanica(AT)nps.edu), Sep 19 2008
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EXTENSIONS
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a(16) - a(47) from Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 04 2009
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