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A094373
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Expansion of (1-x-x^2)/((1-x)*(1-2*x)).
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16
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1, 2, 3, 5, 9, 17, 33, 65, 129, 257, 513, 1025, 2049, 4097, 8193, 16385, 32769, 65537, 131073, 262145, 524289, 1048577, 2097153, 4194305, 8388609, 16777217, 33554433, 67108865, 134217729, 268435457, 536870913, 1073741825, 2147483649, 4294967297, 8589934593
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Partial sum of 1,1,1,2,4,8,... Binomial transform of abs(A073097). Binomial transform is A094374.
Partial sums are in A006127. - Paul Barry (pbarry(AT)wit.ie), Aug 05 2004
Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Aug 15 2010: (Start)
An elephant sequence, see A175654. For the corner squares four A[5] vectors, with decimal values 2, 8, 32 and 128, lead to this sequence. For the central square these vectors lead to the companion sequence A011782.
(End)
This sequence has a(0) = 1 and for all n > 0, a(n) = 2^(n-1)+1. Consequently 2*a(n) >= a(n+1) for all n > 0 and the sequence is complete. [Frank M Jackson, Jan 29 2012]
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Eric Weisstein, Complete Sequence.
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FORMULA
| a(n) = (2^n-0^n)/2+1.
a(n) = +3*a(n-1) -2*a(n-2).
a(2*n) = 2*a(2*n-1)-1, n>0.
Row sums of triangle A135225 - Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 23 2007
a(n) = A131577(n) + 1. - Paul Curtz (bpcrtz(AT)free.fr), Aug 07 2008
a(n)=2*a(n-1)-1 for n>1, a(0)=1, a(1)=2. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 25 2009]
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MATHEMATICA
| CoefficientList[Series[(1 - x - x^2)/((1 - x)*(1 - 2*x)), {x, 0, 40}], x] (* and *) Join[{1}, LinearRecurrence[{3, -2}, {2, 3}, 40]]
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PROG
| (MAGMA) [(2^n-0^n)/2+1: n in [0..40]]; // Vincenzo Librandi, Jun 10 2011
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CROSSREFS
| Apart from the initial 1, identical to A000051.
Cf. A135225.
Sequence in context: A091697 A109740 A000051 * A061902 A166286 A179807
Adjacent sequences: A094370 A094371 A094372 * A094374 A094375 A094376
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KEYWORD
| easy,nonn,changed
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Apr 28 2004
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