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
E.g.f.: 2 + 2*exp(x)*(x - 1) + x. - Stefano Spezia, Jun 16 2024
MAPLE
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
KEYWORD
easy,nonn
AUTHOR
STATUS
approved