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A131577 Zero followed by powers of 2 (cf. A000079). 61
0, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824, 2147483648, 4294967296, 8589934592 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

A000079 is the main entry for this sequence.

Binomial transform of A000035.

Sequence is identical to its second differences.

Essentially the same as A034008 (and A000079).

a(n) = a(n-1)-th even natural numbers (A005846) for n > 1. [From Jaroslav Krizek, Apr 25 2009]

Where record values greater than 1 occur in A083662: A000045(n)=A083662(a(n)). [From Reinhard Zumkeller, Sep 26 2009]

Number of compositions of natural number n into parts >0.

The signed sequence 0, 1, -2, 4, -8, 16, -32, 64, -128, 256, -512, 1024,... is the Lucas U(-2,0) sequence. - R. J. Mathar, Jan 08 2013

In computer programming, these are the only unsigned numbers such that k&(k-1)=0, where & is the bitwise AND operator and numbers are expressed in binary. - Stanislav Sykora, Nov 29 2013

Also the 0-additive sequence: a(n) is the smallest number larger than a(n-1) which is not the sum of any subset of earlier terms, with initial values {0, 1, 2}. - Robert G. Wilson v, Jul 12 2014

REFERENCES

Mohammad K. Azarian, A Generalization of the Climbing Stairs Problem, Mathematics and Computer Education Journal, Vol. 31, No. 1, pp. 24-28, Winter 1997.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Adi Dani, Compositions of natural numbers over arithmetic progressions

Wikipedia, Lucas sequence

Index entries for sequences related to linear recurrences with constant coefficients, signature (2).

Index entries for Lucas sequences

FORMULA

Floor(2^(k-1)) with k=-1..n. - Robert G. Wilson v

G.f.: x/(1-2*x); a(n) = (2^n-0^n)/2. - Paul Barry, Jan 05 2009

E.g.f.: exp(x)*sinh(x). - Geoffrey Critzer, Oct 28 2012

E.g.f.: x/T(0) where T(k) = 4*k+1 - x/(1 + x/(4*k+3 - x/(1 + x/T(k+1) ))); (continued fraction). - Sergei N. Gladkovskii, Mar 17 2013

MAPLE

A131577 := proc(n)

    if n =0 then

        0;

    else

        2^(n-1) ;

    end if;

end proc: # R. J. Mathar, Jul 22 2012

MATHEMATICA

Floor[2^Range[-1, 33]] (* Robert G. Wilson v *)

Join[{0}, 2^Range[0, 60]] (* Vladimir Joseph Stephan Orlovsky, Jun 09 2011 *)

PROG

(MAGMA) [(2^n-0^n)/2: n in [0..50]]; // Vincenzo Librandi, Aug 10 2011

(C) int is (unsigned long n) { return !(n & (n-1)); } /* Charles R Greathouse IV, Sep 15 2012 */

(PARI) a(n)=1<<n-- \\ Charles R Greathouse IV, Sep 15 2012

(Haskell)

a131577 = (`div` 2) . a000079

a131577_list = 0 : a000079_list  -- Reinhard Zumkeller, Dec 09 2012

CROSSREFS

Cf. A000079, A003945, A042950, A020406, A046045, A011782.

Sequence in context: A120617 * A155559 A171449 A122803 A050732 A138815

Adjacent sequences:  A131574 A131575 A131576 * A131578 A131579 A131580

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Aug 29 2007, Dec 06 2007

EXTENSIONS

More terms from Robert G. Wilson v, Sep 02 2007

Edited by N. J. A. Sloane, Sep 13 2007

STATUS

approved

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Last modified October 22 10:00 EDT 2014. Contains 248391 sequences.