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A052928 The even numbers repeated. 27
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

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

W. Eisfeld and A. Viel, Higher order (A+E)xe pseudo-Jahn-Teller coupling, J. Chem. Phys., 122, 204317 (2005).

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 914

J. Sondow and E. W. Weisstein, MathWorld: Wallis Formula

Eric Weisstein's World of Mathematics, Random Matrix

Eric Weisstein's World of Mathematics, Legendre-Gauss Quadrature

Index entries for linear recurrences with constant coefficients, signature (1,1,-1)

Index entries for Molien series

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

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 *)

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, A008619, A032766, A064455, A109613, A123684.

Sequence in context: A061106 A161764 A131055 * A137501 A005186 A259881

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 September 3 08:46 EDT 2015. Contains 261314 sequences.