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A052928
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The even numbers repeated.
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18
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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; internal format)
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OFFSET
| 0,3
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COMMENTS
| a(n) is also the binary rank of the complete graph K(n) [From Alessandro Cosentino (cosenal(AT)gmail.com), Feb 07 2009]
Its ordinal transform is A000034 [From Paolo P. Lava (paoloplava(AT)gmail.com), Jun 25 2009]
Let I=I_n be the nXn 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) nXn matrices A<=P^(-1)+I+P having exactly two 1's in every row and column with perA=2. [From Vladimir Shevelev (shevelev(AT)bgu.ac.il), Apr 12 2010]
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REFERENCES
| C. D. Godsil and G. Royle, Algebraic Graph Theory, Springer, 2001, pag.181 [From 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. [From Vladimir Shevelev (shevelev(AT)bgu.ac.il), Apr 12 2010]
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 914
Eric Weisstein's World of Mathematics, Wallis Formula
Eric Weisstein's World of Mathematics, Random Matrix
Eric Weisstein's World of Mathematics, Legendre-Gauss Quadrature
Index to sequences with linear recurrences with constant coefficients, signature (1,1,-1)
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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 (fynmun(AT)hotmail.com), Mar 20 2008
a(n) = a(n-1)+a(n-2)-a(n-3). [R. J. Mathar (mathar(at)strw.leidenunvi.nl), 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)). [From 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. - From DELEHAM Philippe, Oct 19 2011.
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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);
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PROG
| (PARI) a(n)=n\2*2 \\ Charles R Greathouse IV, Nov 20 2011
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CROSSREFS
| Sequence in context: A061106 A161764 A131055 * A137501 A005186 A008642
Adjacent sequences: A052925 A052926 A052927 * A052929 A052930 A052931
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KEYWORD
| easy,nonn
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AUTHOR
| encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jun 05 2000
Removed duplicate of recurrence; corrected original recurrence and g.f. against offset - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 19 2010
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