

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
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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



