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A004396
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One even number followed by two odd numbers.
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22
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0, 1, 1, 2, 3, 3, 4, 5, 5, 6, 7, 7, 8, 9, 9, 10, 11, 11, 12, 13, 13, 14, 15, 15, 16, 17, 17, 18, 19, 19, 20, 21, 21, 22, 23, 23, 24, 25, 25, 26, 27, 27, 28, 29, 29, 30, 31, 31, 32, 33, 33, 34, 35, 35, 36, 37, 37, 38, 39, 39, 40, 41, 41, 42, 43, 43, 44, 45, 45, 46, 47, 47
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Maximal number of points on a chunk of triangular grid of edge length n with no 2 points on same line. Generalized from Problem 252 in Loren Larson's translation of Paul Vaderlind's book- R. K. Guy.
Apart from initial term(s), dimension of the space of weight 2n cusp forms for Gamma_0( 3 ).
Starting at 3,3,..., gives maximal number of acute angles in an n-gon. - Takenov Nurdin (takenov_vert(AT)e-mail.ru), Mar 04 2003
Let b(1)=b(2)=1, b(k) = b(k-1)+( b(k-2) reduced (mod 2)); then a(n) = b(n-1). - Benoit Cloitre, Aug 14 2002
(1+x+x^2+x^3 ) / ( (1-x^2)*(1-x^3)) is the Poincare series (or Molien series) for Sigma_4.
a(n) = A096777(n+1) - A096777(n) for n>0. - Reinhard Zumkeller, Jul 09 2004
For n>6, maximum number of knight moves to reach any square from the corner of an (n-2) X (n-2) chessboard. Likewise for n>6, the maximum number of knight moves to reach any square from the middle of an (2n-5) X (2n-5) chessboard. - R. Stephan, Sep 15 2004
A transform of the Jacobsthal numbers A001045 under the mapping of g.f.s g(x)->g(x/(1+x^2)). - Paul Barry, Jan 16 2005
a(A032766(n)) = n. [From Reinhard Zumkeller, Oct 30 2009]
For n >= 1; a(n) = number of successive terms of A040001 that add to n; or length of n-th term of A028359. [From Jaroslav Krizek, Mar 28 2010]
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REFERENCES
| A. Adem and R. J. Milgram, Cohomology of Finite Groups, Springer-Verlag, 2nd. ed., 2004; p. 246.
J. Kurschak, Hungarian Mathematical Olympiads, 1976, Mir, Moscow.
C. L. Mallows and N. J. A. Sloane, Weight enumerators of self-orthogonl codes, Discrete Math., 9 (1974), 391-400 (see proof of Theorem 1).
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Art of Problem Solving Forum, Ordered triples choosing - From Joel Brewster Lewis (jblewis(AT)post.harvard.edu), May 21 2009
John A. Pelesko, Generalizing the Conway-Hofstadter $10,000 Sequence, Journal of Integer Sequences, Vol. 7 (2004), Article 04.3.5.
William A. Stein, Dimensions of the spaces S_k(Gamma_0(N))
William A. Stein, The modular forms database
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FORMULA
| G.f.: (x+x^3)/((1-x)*(1-x^3)).
a(n) = floor( (2*n + 1)/3 )
a(n) = a(n-1) + (1/2)*((-1)^floor((4*n+2)/3) + 1), a(0)=0. - Mario Catalani (mario.catalani(AT)unito.it), Oct 20 2003
a(n) = 2n/3-cos(2*pi*n/3+pi/3)/3+sqrt(3)sin(2*pi*n/3+pi/3)/9. - Paul Barry, Mar 18 2004
G.f.: x*(1+x^2)/(1-x-x^3+x^4); a(n)=a(n-1)+a(n-3)-a(n-4); a(n)=sum{k=0..n, binomial(n-k-1, k)(-1)^k*A001045(n-2k)}; - Paul Barry, Jan 16 2005
a(n) = (A006369(n) - (A006369(n) mod 2) * (-1)^(n mod 3)) / (1 + A006369(n) mod 2). - Reinhard Zumkeller, Jan 23 2005
a(n) = A004773(n) - A004523(n). - Reinhard Zumkeller, Aug 29 2005
a(n) = floor(n/3) + ceiling(n/3). - Jonathan Vos Post, Mar 19 2006
a(n+1)=A008620(2n) . - Philippe DELEHAM, Dec 14 2006
a(n)=floor((2*n^2+4*n+2)/(3*n+4)) [From Gary Detlefs, Jul 13 2010]
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MATHEMATICA
| Table[ Floor[(2n + 1)/3], {n, 0, 75} ]
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PROG
| (MAGMA) [(Floor(n/3) + Ceiling(n/3)): n in [0..70]]; // Vincenzo Librandi, Aug 07 2011
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CROSSREFS
| Cf. A004523, A002620.
Sequence in context: A093878 A156689 A168052 * A131737 A066481 A121928
Adjacent sequences: A004393 A004394 A004395 * A004397 A004398 A004399
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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