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A004277
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1 together with positive even numbers.
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36
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1, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132
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OFFSET
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0,2
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COMMENTS
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Also number of non-attacking bishops on n X n board. - Koksal Karakus (karakusk(AT)hotmail.com), May 27 2002
Engel expansion of e^(1/2) (see A006784 for definition) [when offset by 1]. - Henry Bottomley, Dec 18 2000
Numbers n such that a 2n-group (i.e., a group of order 2n) has subgroup C_2. - Lekraj Beedassy, Oct 14 2004
Image of 1/(1-2x) under the mapping g(x)->g(x/(1+x^2)). - Paul Barry, Jan 16 2005
Position of n in A113322: A113322(a(n-1)) = n for n>0. - Reinhard Zumkeller, Oct 26 2005
Incrementally largest terms in the continued fraction for e. - Nick Hobson, Jan 11 2007
Conjecturally, the differences of two consecutive primes (without repetition). - Juri-Stepan Gerasimov, Nov 09 2009
Equals (1, 2, 2, 2,...) convolved with (1, 0, 2, 0, 2, 0, 2,...). - Gary W. Adamson, Mar 03 2010
a(n) is the number of 0-dimensional elements (vertices) in an n-cross polytope. - Patrick J. McNab, Jul 06 2015
Numbers k such that in the symmetric representation of sigma(k) there is no pair bars as its ends (Cf. A237593). - Omar E. Pol, Sep 28 2018
Also, the coordination sequence of the L-lattice (see A332419). - Sean A. Irvine, Jul 29 2020
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LINKS
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Table of n, a(n) for n=0..66.
E. Friedman, Math. Magic
Eric Weisstein's World of Mathematics, Cross Polytope
Index entries for sequences related to Engel expansions
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FORMULA
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G.f.: (1+x^2)/(1-x)^2. - Paul Barry, Feb 28 2003
Inverse binomial transform of Cullen numbers A002064. a(n)=2n+0^n. - Paul Barry, Jun 12 2003
a(n) = sum{k=0..floor(n/2), binomial(n-k-1)(-1)^k*2^(n-2k)}. - Paul Barry, Jan 16 2005
Equals binomial transform of [1, 1, 1, -1, 1, -1, 1,...]. - Gary W. Adamson, Jul 15 2008
E.g.f.: 1+x*sinh(x) (aerated sequence). - Paul Barry, Oct 11 2009
a(n) = 0^n + 2*n = A000007(n) + A005843(n). - Reinhard Zumkeller, Jan 11 2012
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MATHEMATICA
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Join[{1}, Table[2*n, {n, 200}]] (* Vladimir Joseph Stephan Orlovsky, Jul 10 2011 *)
Select[Range@ 105, PowerMod[#, #, # + 1] == 1 &] (* Robert G. Wilson v, Sep 26 2016 *)
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PROG
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(Haskell)
a004277 n = 2 * n - 1 + signum (1 - n)
a004277_list = 1 : [2, 4 ..] -- Reinhard Zumkeller, Dec 19 2013
(MAGMA) [1] cat [2*n: n in [1..80]]; // Vincenzo Librandi, Jul 11 2015
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CROSSREFS
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Cf. A004275, A008486, A030978, A097134.
INVERT transformation yields A098182 without A098182(0). - R. J. Mathar, Sep 11 2008
Sequence in context: A317108 A317440 A076032 * A299174 A122080 A105360
Adjacent sequences: A004274 A004275 A004276 * A004278 A004279 A004280
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KEYWORD
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easy,nonn
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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Corrected by Charles R Greathouse IV, Mar 18 2010
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STATUS
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approved
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