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A131577
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Zero followed by powers of 2 (cf. A000079).
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50
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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; internal format)
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OFFSET
| 0,3
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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
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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.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Adi Dani, Compositions of natural numbers over arithmetic progressions
Index entries for sequences related to linear recurrences with constant coefficients, signature (2).
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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; [From Paul Barry, Jan 05 2009]
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MATHEMATICA
| t = Table[ Floor[2^n], {n, -1, 34}]; d1 = Rest@t - Most@t; d2 = Rest@d1 - Most@d1 (* Robert G. Wilson v *)
Join[{0}, 2^Range[0, 60]] (* From Vladimir Joseph Stephan Orlovsky, June 09 2011 *)
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PROG
| (MAGMA) [(2^n-0^n)/2: n in [0..50]]; // Vincenzo Librandi, Aug 10 2011
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CROSSREFS
| Cf. A000079, A003945, A042950, A020406, A046045, A011782.
Sequence in context: A000079 A120617 * A171449 A050732 A138815 A180212
Adjacent sequences: A131574 A131575 A131576 * A131578 A131579 A131580
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KEYWORD
| nonn,easy
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AUTHOR
| Paul Curtz (bpcrtz(AT)free.fr), Aug 29 2007, Dec 06 2007
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 02 2007
Edited by N. J. A. Sloane (njas(AT)research.att.com), Sep 13 2007
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