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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 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 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 Adjacent sequences: A004272 A004273 A004274 * A004276 A004277 A004278 KEYWORD easy,nonn,changed AUTHOR N. J. A. Sloane STATUS approved

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