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A004275 1 together with nonnegative even numbers. 45
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 (list; graph; refs; listen; history; text; internal format)
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
Megan A. Martinez and Carla D. Savage, Patterns in Inversion Sequences II: Inversion Sequences Avoiding Triples of Relations, arXiv:1609.08106 [math.CO], 2016.
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
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: A366846 A119432 A005843 * A317108 A317440 A076032
KEYWORD
easy,nonn,changed
AUTHOR
STATUS
approved

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Last modified June 25 18:08 EDT 2024. Contains 373707 sequences. (Running on oeis4.)