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A050291 Number of double-free subsets of {1, 2, ..., n}. 11
2, 3, 6, 10, 20, 30, 60, 96, 192, 288, 576, 960, 1920, 2880, 5760, 9360, 18720, 28080, 56160, 93600, 187200, 280800, 561600, 898560, 1797120, 2695680, 5391360, 8985600, 17971200, 26956800, 53913600, 87091200, 174182400, 261273600 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A set is double-free if it does not contain both x and 2x.

REFERENCES

Wang, E. T. H. ``On Double-Free Sets of Integers.'' Ars Combin. 28, 97-100, 1989.

LINKS

T. D. Noe, Table of n, a(n) for n = 1..400

S. R. Finch, Triple-Free Sets of Integers

Eric Weisstein's World of Mathematics, Double-Free Set.

FORMULA

a(n) = a(n-1)*Fib(b(2n)+2)/Fib(b(2n)+1), Fib = A000045, b = A007814.

a(n) = 2^n - A088808(n). - Reinhard Zumkeller, Oct 19 2003

MATHEMATICA

a[n_] := a[n] = (b = IntegerExponent[2n, 2]; a[n-1]*Fibonacci[b+2]/Fibonacci[b+1]); a[1]=2; Table[a[n], {n, 1, 34}] (* Jean-Fran├žois Alcover, Oct 10 2012, from first formula *)

PROG

(PARI) first(n)=my(v=vector(n)); v[1]=2; for(k=2, n, v[k]=v[k-1]*fibonacci(valuation(k, 2)+3)/fibonacci(valuation(k, 2)+2)); v \\ Charles R Greathouse IV, Feb 07 2017

CROSSREFS

Cf. A050292-A050296.

Sequence in context: A247162 A001678 A113292 * A214002 A135452 A077027

Adjacent sequences:  A050288 A050289 A050290 * A050292 A050293 A050294

KEYWORD

nonn,easy,nice

AUTHOR

Eric W. Weisstein

EXTENSIONS

Extended with formula by Christian G. Bower, Sep 15 1999

STATUS

approved

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Last modified July 27 04:53 EDT 2017. Contains 289841 sequences.