A004275 1 together with nonnegative even numbers.

0, 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

Offset: 0

Author

N. J. A. Sloane

Keywords

• easy
• nonn

Comments

A091090(a(n)) = 1. - Reinhard Zumkeller, Mar 13 2011

Base-4 analog of A031149: floor(n^2/4) is a square. - M. F. Hasler, Jan 15 2012

From Eric M. Schmidt, Jul 17 2017: (Start)

Number of sequences (e(1), ..., e(n)), 0 <= e(i) < i, such that there is no triple i < j < k with e(i) != e(j) and e(i) != e(k). [Martinez and Savage, 2.2]

Number of sequences (e(1), ..., e(n)), 0 <= e(i) < i, such that there is no triple i < j < k with e(i) >= e(j) and e(i) != e(k). [Martinez and Savage, 2.2]

(End)

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Megan A. Martinez and Carla D. Savage, Patterns in Inversion Sequences II: Inversion Sequences Avoiding Triples of Relations, arXiv:1609.08106 [math.CO], 2016.
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A004277.

Range of A007457.

Programs

Haskell

a004275 n = 2 * n - 1 + signum (1 - n)
a004275_list = 0 : 1 : [2, 4 ..]  -- Reinhard Zumkeller, Dec 18 2013

Magma

[Floor((2*n^2)/(1 + n)): n in [0..60] ]; // Vincenzo Librandi, Aug 19 2011

Maple

A004275:= n-> 2*n - 2 + floor(2/(n+1)); seq(A004275(k), k=0..100); # Wesley Ivan Hurt, Nov 05 2013

Mathematica

A004275[n_]:=Floor[(2 n^2)/(1 + n)]; (* Enrique Pérez Herrero, Apr 05 2010 *)
Insert[Range[0,110,2],1,2] (* Harvey P. Dale, Feb 27 2015 *)

Formula

G.f.: x*(1+x^2)/(1-x)^2. - Paul Barry, Feb 28 2003

a(n) = floor((2*n^2)/(1 + n)). - Enrique Pérez Herrero, Apr 05 2010

a(n) = 2n - 2 + floor(2/(n+1)) = max(n, 2n-2) = 2n - 1 + sgn(1-n). Also, a(0)=0, a(1)=1, a(n) = 2n-2 for n > 1. - Wesley Ivan Hurt, Nov 05 2013

E.g.f.: 2 + 2*exp(x)*(x - 1) + x. - Stefano Spezia, Jun 16 2024