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A154393 Empirically good sequence of increments for shell sort algorithm. 1
1, 9, 34, 182, 836, 4025, 19001, 90358, 428481, 2034035, 9651787, 45806244, 217378076, 1031612713, 4895689348, 23233383508, 110258103799, 523249458736, 2483172990911, 11784338112247, 55924666344750, 265400424550505, 1259504788813791, 5977203382848010 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This sequence was made by taking the Fibonacci numbers, leaving out one of the starting 1's, raising them to the power of 2 * the golden ratio. Fractions are removed with the floor function. It works particularly well as a gap sequence for the shell sort algorithm on large arrays.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Wikipedia, Shell sort

FORMULA

a(n) = floor(fibonacci(n+1)^(1+sqrt(5))).

MATHEMATICA

Table[Floor[Fibonacci[n + 1]^(1 + Sqrt[5])], {n, 1, 10}] (* G. C. Greubel, Sep 16 2016 *)

CROSSREFS

Sequence in context: A264678 A050478 A204426 * A119389 A197273 A067960

Adjacent sequences:  A154390 A154391 A154392 * A154394 A154395 A154396

KEYWORD

nonn

AUTHOR

Niels Pardons (nielspardons(AT)hotmail.com), Jan 08 2009

EXTENSIONS

More terms from Alois P. Heinz, May 31 2016

STATUS

approved

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Last modified September 19 23:31 EDT 2019. Contains 327207 sequences. (Running on oeis4.)