0,4

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 (benoit7848c(AT)orange.fr), 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 (reinhard.zumkeller(AT)gmail.com), 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 (pbarry(AT)wit.ie), Jan 16 2005

a(A032766(n)) = n. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 30 2009]

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).

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

G.f.: (x+x^3)/((1-x)*(1-x^3)). a(n)=[ (2n+1)/3 ].

a(n) = Floor[(2n + 1)/3]

a(n)=a(n-1)+(1/2)((-1)^Floor[(4n+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 (pbarry(AT)wit.ie), 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 (pbarry(AT)wit.ie), Jan 16 2005

a(n) = (A006369(n) - (A006369(n) mod 2) * (-1)^(n mod 3)) / (1 + A006369(n) mod 2). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jan 23 2005

a(n) = A004773(n) - A004523(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 29 2005

a(n) = floor(n/3) + ceiling(n/3). - Jonathan Vos Post (jvospost3(AT)gmail.com), Mar 19 2006

a(n+1)=A008620(2n) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 14 2006

Table[ Floor[(2n + 1)/3], {n, 0, 75} ]

Cf. A004523, A002620.

Sequence in context: A131138 A093878 A156689 this_sequence A131737 A066481 A121928

Adjacent sequences: A004393 A004394 A004395 this_sequence A004397 A004398 A004399

nonn,new

N. J. A. Sloane (njas(AT)research.att.com).