A052928 The even numbers repeated.
0, 0, 2, 2, 4, 4, 6, 6, 8, 8, 10, 10, 12, 12, 14, 14, 16, 16, 18, 18, 20, 20, 22, 22, 24, 24, 26, 26, 28, 28, 30, 30, 32, 32, 34, 34, 36, 36, 38, 38, 40, 40, 42, 42, 44, 44, 46, 46, 48, 48, 50, 50, 52, 52, 54, 54, 56, 56, 58, 58, 60, 60, 62, 62, 64, 64, 66, 66, 68, 68, 70, 70, 72, 72
Offset: 0
References
- C. D. Godsil and G. Royle, Algebraic Graph Theory, Springer, 2001, page 181. - Alessandro Cosentino (cosenal(AT)gmail.com), Feb 07 2009
- V. S. Shevelyov (Shevelev), Extension of the Moser class of four-line Latin rectangles, DAN Ukrainy, 3(1992),15-19.
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- C. Beierle, A. Biryukov and A. Udovenko, On degree-d zero-sum sets of full rank, Cryptography and Communications, November 2019.
- W. Eisfeld and A. Viel, Higher order (A+E)xe pseudo-Jahn-Teller coupling, J. Chem. Phys., 122, 204317 (2005).
- Nathan Fox, Finding Linear-Recurrent Solutions to Hofstadter-Like Recurrences Using Symbolic Computation, arXiv:1609.06342 [math.NT], 2016.
- INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 914
- J. Sondow and E. W. Weisstein, MathWorld: Wallis Formula
- Eric Weisstein's World of Mathematics, Chromatic Number
- Eric Weisstein's World of Mathematics, Legendre-Gauss Quadrature
- Eric Weisstein's World of Mathematics, Maximum Vertex Degree
- Eric Weisstein's World of Mathematics, Polygon Diagonal Intersection Graph
- Eric Weisstein's World of Mathematics, Random Matrix
- Eric Weisstein's World of Mathematics, White Bishop Graph
- Index entries for linear recurrences with constant coefficients, signature (1,1,-1)
- Index entries for Molien series
Crossrefs
Cf. A000034, A000124, A004001, A004526, A005843, A007590, A008619, A008794, A032766, A064455, A099392, A109613, A118266, A123684, A124356, A192442, A289187, A342819.
For n >= 3, A329822(n) gives the minimum weight of a Boolean function of algebraic degree at most n-3 whose support contains n linearly independent elements. - Christof Beierle, Nov 25 2019
Programs
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Haskell
a052928 = (* 2) . flip div 2 a052928_list = 0 : 0 : map (+ 2) a052928_list -- Reinhard Zumkeller, Jun 20 2015
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Magma
[2*Floor(n/2) : n in [0..50]]; // Wesley Ivan Hurt, Sep 13 2014
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Maple
spec := [S,{S=Union(Sequence(Prod(Z,Z)),Prod(Sequence(Z),Sequence(Z)))},unlabeled]: seq(combstruct[count](spec,size=n), n=0..20); -
Mathematica
Flatten[Table[{2n, 2n}, {n, 0, 39}]] (* Alonso del Arte, Jun 24 2012 *) With[{ev=2Range[0,40]},Riffle[ev,ev]] (* Harvey P. Dale, May 08 2021 *) Table[Round[n + 1/2], {n, -1, 72}] (* Ed Pegg Jr, Jul 28 2025 *) -
PARI
a(n)=n\2*2 \\ Charles R Greathouse IV, Nov 20 2011
Formula
a(n) = 2*floor(n/2).
G.f.: 2*x^2/((-1+x)^2*(1+x)).
a(n) + a(n+1) + 2 - 2*n = 0.
a(n) = n - 1/2 + (-1)^n/2.
a(n) = n + Sum_{k=1..n} (-1)^k. - William A. Tedeschi, Mar 20 2008
a(n) = a(n-1) + a(n-2) - a(n-3). - R. J. Mathar, Feb 19 2010
For n > 0, a(n) = floor(sqrt(n^2+(-1)^n)). - Francesco Daddi, Aug 02 2011
a(n) = Sum_{k>=0} A030308(n,k)*b(k) with b(0)=0 and b(k)=2^k for k>0. - Philippe Deléham, Oct 19 2011
a(n) = A109613(n) - 1. - M. F. Hasler, Oct 22 2012
a(n) = n - (n mod 2). - Wesley Ivan Hurt, Jun 29 2013
a(n) = a(a(n-1)) + a(n-a(n-1)) for n>2. - Nathan Fox, Jul 24 2016
a(n) = 2*A004526(n). - Filip Zaludek, Oct 28 2016
E.g.f.: x*exp(x) - sinh(x). - Ilya Gutkovskiy, Oct 28 2016
From Guenther Schrack, May 29 2019: (Start)
a(b(n)) = b(n) + ((-1)^b(n) - 1)/2 for any sequence b(n) of offset 0.
a(a(n)) = a(n), idempotent.
a(n)*a(n+1)/2 = A007590(n), also equals partial sums of a(n).
Extensions
More terms from James Sellers, Jun 05 2000
Removed duplicate of recurrence; corrected original recurrence and g.f. against offset - R. J. Mathar, Feb 19 2010
Comments