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 A052928 The even numbers repeated. 54
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(n) is also the binary rank of the complete graph K(n). - Alessandro Cosentino (cosenal(AT)gmail.com), Feb 07 2009 Its ordinal transform is A000034. - Paolo P. Lava, Jun 25 2009 Let I=I_n be the n X n identity matrix and P=P_n be the incidence matrix of the cycle (1,2,3,...,n). Then, for n >= 6, a(n) is the number of (0,1) n X n matrices A <= P^(-1)+I+P having exactly two 1's in every row and column with perA=2. - Vladimir Shevelev, Apr 12 2010 a(n+2) is the number of symmetry allowed, linearly independent terms at n-th order in the series expansion of the (E+A)xe vibronic perturbation matrix, H(Q) (cf. Eisfeld & Viel). - Bradley Klee, Jul 21 2015 The arithmetic function v_2(n,1) as defined in A289187. - Robert Price, Aug 22 2017 For n > 1, also the chromatic number of the n X n white bishop graph. - Eric W. Weisstein, Nov 17 2017 For n > 2, also the maximum vertex degree of the n-polygon diagonal intersection graph. - Eric W. Weisstein, Mar 23 2018 For n >= 2, a(n+2) gives the minimum weight of a Boolean function of algebraic degree at most n-2 whose support contains n linearly independent elements. - Christof Beierle, Nov 25 2019 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) 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 a(n) = |A123684(n) - A064455(n)| = A032766(n) - A008619(n-1). - Jaroslav Krizek, Mar 22 2011 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 a(-n) = -a(n+1); a(n) = A005843(A004526(n)). - Guenther Schrack, Sep 11 2018 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(A086970(n)) = A124356(n-1) for n > 1. a(A000124(n)) = A192447(n+1). a(n)*a(n+1)/2 = A007590(n), also equals partial sums of a(n). A007590(a(n)) = 2*A008794(n). (End) 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 *) PROG (PARI) a(n)=n\2*2 \\ Charles R Greathouse IV, Nov 20 2011 (MAGMA) [2*Floor(n/2) : n in [0..50]]; // Wesley Ivan Hurt, Sep 13 2014 (Haskell) a052928 = (* 2) . flip div 2 a052928_list = 0 : 0 : map (+ 2) a052928_list -- Reinhard Zumkeller, Jun 20 2015 CROSSREFS Cf. A000034, A000124, A004001, A004526, A005843, A007590, A008619, A008794, A032766, A064455, A099392, A109613, A118266, A123684, A124356, A192442, A289187, A342819. First differences: A010673; partial sums: A007590; partial sums of partial sums: A212964(n+1). Complement of A109613 with respect to universe A004526. - Guenther Schrack, Dec 07 2017 Is first differences of A099392. Fixed point sequence: A005843. - Guenther Schrack, May 30 2019 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 Sequence in context: A161764 A293706 A131055 * A137501 A308767 A345419 Adjacent sequences:  A052925 A052926 A052927 * A052929 A052930 A052931 KEYWORD nonn,easy AUTHOR encyclopedia(AT)pommard.inria.fr, Jan 25 2000 EXTENSIONS More terms from James A. Sellers, Jun 05 2000 Removed duplicate of recurrence; corrected original recurrence and g.f. against offset - R. J. Mathar, Feb 19 2010 STATUS approved

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Last modified July 27 01:40 EDT 2021. Contains 346302 sequences. (Running on oeis4.)