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1, 1, 3, 6, 13, 27, 56, 115, 235, 478, 969, 1959, 3952, 7959, 16007, 32158, 64549, 129475, 259560, 520107, 1041811, 2086206, 4176593, 8359951, 16730848, 33479407, 66987471, 134021310, 268117645, 536356683, 1072909784, 2146137379
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Binomial transform of (-1)^n*Fib(n)+1=(-1)^n*A008346(n).
Number of compositions of n+1 that contain 1 as a part. - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 26 2004
Generated from iterates of M * [1,1,1,...], where M = a tridiagonal matrix with [0,1,1,1,...] as the main diagonal, [1,1,1,...] as the superdiagonal and [1,0,0,0,...] as the subdiagonal. [From Gary W. Adamson, Jan 05 2009]
Starting with offset 1, generated from iterates of M * [1,1,1,...], M*ANS -> M*ANS,...; where M = = a tridiagonal matrix with (0,1,1,1,...) in the main diagonal, (1,1,1,...) in the superdiagonal and (1,0,0,0,...) in the subdiagonal. [From Gary W. Adamson, Jan 04 2009]
Contribution from Johannes W. Meijer, Aug 15 2010: (Start)
An elephant sequence, see A175655. For the central square 24 A[5] vectors, with decimal values between 11 and 416, lead to this sequence (without the first leading 1). For the corner squares these vectors lead to the companion sequence A027934 (without the leading 0). (End)
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..200
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FORMULA
| G.f.: (1-x)^2/((1-2x)(1-x-x^2)); a(n)=3a(n-1)-a(n-2)-2a(n-3).
a(n) = A101220(1, 2, n+1) - A101220(1, 2, n). - Ross La Haye (rlahaye(AT)new.rr.com), Aug 05 2005
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MATHEMATICA
| Table[2^n-Fibonacci[n], {n, 0, 100}] (* From Vladimir Joseph Stephan Orlovsky, May 02 2011 *)
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PROG
| (MAGMA) [2^n-Fibonacci(n): n in [0..35]]; // Vincenzo Librandi, May 03 2011
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CROSSREFS
| Cf. A000045.
Sequence in context: A055143 A092539 A094386 * A131246 A183314 A036886
Adjacent sequences: A099033 A099034 A099035 * A099037 A099038 A099039
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Sep 23 2004
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EXTENSIONS
| More terms from Ross La Haye (rlahaye(AT)new.rr.com), Aug 05 2005
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