A004277 1 together with positive even numbers.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• easy
• nonn

Comments

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

Links

• E. Friedman, Math. Magic
• Eric Weisstein's World of Mathematics, Cross Polytope
• Index entries for sequences related to Engel expansions
• Index entries for linear recurrences with constant coefficients, signature (2, -1).

Crossrefs

Cf. A004275, A008486, A030978, A097134.

INVERT transformation yields A098182 without A098182(0). - R. J. Mathar, Sep 11 2008

Programs

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

Mathematica

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 *)

Formula

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

Extensions

Corrected by Charles R Greathouse IV, Mar 18 2010