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A052551
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Expansion of 1/((1-x)(1-2x^2)).
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7
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1, 1, 3, 3, 7, 7, 15, 15, 31, 31, 63, 63, 127, 127, 255, 255, 511, 511, 1023, 1023, 2047, 2047, 4095, 4095, 8191, 8191, 16383, 16383, 32767, 32767, 65535, 65535, 131071, 131071, 262143, 262143, 524287, 524287, 1048575, 1048575, 2097151, 2097151
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Equals row sums of triangle A137865. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 18 2008
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..2000
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 488
Index to sequences with linear recurrences with constant coefficients, signature (1,2,-2).
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FORMULA
| G.f.: 1/(-1+2*x^2)/(-1+x)
Recurrence: {a(1)=1, a(0)=1, -2*a(n)-1+a(n+2)=0.}
-1+Sum(1/2*(1+2*_alpha)*_alpha^(-1-n), _alpha=RootOf(-1+2*_Z^2))
a(n)=A016116(n+2)-1. [From R. J. Mathar, Jun 15 2009]
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MAPLE
| spec := [S, {S=Prod(Sequence(Prod(Z, Union(Z, Z))), Sequence(Z))}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);
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MATHEMATICA
| a=0; b=1; lst={b}; Do[c=a+b-(b-a-1); AppendTo[lst, c]; a=b; b=c, {n, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 23 2009]
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PROG
| (MAGMA) [2^Floor(n/2)-1: n in [2..50]]; // Vincenzo Librandi, Aug 16 2011
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CROSSREFS
| Cf. A136865.
Sequence in context: A147449 A086530 A147402 * A147096 A147252 A147104
Adjacent sequences: A052548 A052549 A052550 * A052552 A052553 A052554
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KEYWORD
| easy,nonn
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AUTHOR
| encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jun 06 2000
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