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A083329
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a(0) = 1; for n > 0, 3*2^(n-1) - 1.
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18
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1, 2, 5, 11, 23, 47, 95, 191, 383, 767, 1535, 3071, 6143, 12287, 24575, 49151, 98303, 196607, 393215, 786431, 1572863, 3145727, 6291455, 12582911, 25165823, 50331647, 100663295, 201326591, 402653183, 805306367, 1610612735, 3221225471
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Apart from leading term (which should really be 3/2), same as A055010.
Binomial transform of A040001. Inverse binomial transform of A053156.
a(n) = A105728(n+1,2). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 18 2005
a(n) = number of partitions pi of [n+1] (in standard increasing form) such that the permutation Flatten[pi] avoids the patterns 2-1-3 and 3-1-2. Example: a(3)=11 counts all 15 partitions of [4] except 13/24, 13/2/4 which contain a 2-1-3 and 14/23, 14/2/3 which contain a 3-1-2. Here "standard increasing form" means the entries are increasing in each block and the blocks are arranged in increasing order of their first entries. - David Callan (callan(AT)stat.wisc.edu), Jul 22 2008
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 42, 138, 162, 168, lead to this sequence. For the central square these vectors lead to the companion sequence A003945.
(End)
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LINKS
| Eric Weisstein's World of Mathematics, Mycielski Graph [From Eric W. Weisstein (eric(AT)weisstein.com), Nov 24 2008]
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FORMULA
| a(n)=(3*2^n-2+0^n)/2. G.f.: (1-x+x^2)/((1-x)(1-2x)). E.g.f.: (3exp(2x)-2exp(x)+exp(0))/2
a(0) = 1, a(n) = sum of all previous terms + n. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jun 20 2004
Row sums of triangle A133567 - Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 16 2007
Row sums of triangle A135226 - Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 23 2007
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EXAMPLE
| a(0)=(3*2^0-2+0^0)/2=2/2=1 (use 0^0=1).
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MAPLE
| seq(ceil((2^i+2^(i+1)-2)/2), i=0..31); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 02 2007
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MATHEMATICA
| a[1] = 2; a[n_] := 2a[n - 1] + 1; Table[ a[n], {n, 31}] (from Robert G. Wilson v May 04 2004)
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CROSSREFS
| Essentially the same as A055010 and A052940.
Cf. A133567.
Cf. A135226.
Sequence in context: A086219 A055010 * A153893 A081973 A055496 A105120
Adjacent sequences: A083326 A083327 A083328 * A083330 A083331 A083332
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Apr 27 2003
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EXTENSIONS
| The generating function corrected by Martin Griffiths (griffm(AT)essex.ac.uk), Dec 01 2009
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