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A052928
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The even numbers repeated.
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65
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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
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OFFSET
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0,3
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COMMENTS
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a(n) is also the binary rank of the complete graph K(n). - Alessandro Cosentino (cosenal(AT)gmail.com), Feb 07 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
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
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REFERENCES
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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.
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LINKS
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FORMULA
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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) = a(n-1) + a(n-2) - a(n-3). - R. J. Mathar, Feb 19 2010
a(n) = a(a(n-1)) + a(n-a(n-1)) for n>2. - Nathan Fox, Jul 24 2016
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).
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MAPLE
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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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MATHEMATICA
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With[{ev=2Range[0, 40]}, Riffle[ev, ev]] (* Harvey P. Dale, May 08 2021 *)
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PROG
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(Haskell)
a052928 = (* 2) . flip div 2
a052928_list = 0 : 0 : map (+ 2) a052928_list
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CROSSREFS
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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
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KEYWORD
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nonn,easy
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AUTHOR
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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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EXTENSIONS
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Removed duplicate of recurrence; corrected original recurrence and g.f. against offset - R. J. Mathar, Feb 19 2010
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STATUS
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approved
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