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

Offset

0,3

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).

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

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 *)

Prog

(Magma) [Floor((2*n^2)/(1 + n)): n in [0..60] ]; // Vincenzo Librandi, Aug 19 2011
(Haskell)
a004275 n = 2 * n - 1 + signum (1 - n)
a004275_list = 0 : 1 : [2, 4 ..]  -- Reinhard Zumkeller, Dec 18 2013

Crossrefs

Cf. A004277.

Range of A007457.

Sequence in context: A055966 A087113 A366846 * A119432 A005843 A317108

Adjacent sequences: A004272 A004273 A004274 * A004276 A004277 A004278

Keyword

easy,nonn

Author

N. J. A. Sloane

Status

approved