0,4

Arises from Gleason's theorem on self-dual codes: the Molien series is 1/((1-x^8)*(1-x^24)) for the weight enumerators of doubly-even binary self-dual codes; also 1/((1-x^4)*(1-x^12)) for ternary self-dual codes.

a(n) = A001840(n+1) - A001840(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 01 2002

The number of partitions of n into distinct parts where each part is either a power of two or three times a power of two.

G. E. Andrews, K. Eriksson, Integer Partitions, Cambridge Univ. Press, 2004. page 12 Exer. 7

D. J. Benson, Polynomial Invariants of Finite Groups, Cambridge, 1993, p. 100.

E. R. Berlekamp, F. J. MacWilliams and N. J. A. Sloane, Gleason's Theorem on Self-Dual Codes, IEEE Trans. Information Theory, IT-18 (1972), 409-414.

F. J. MacWilliams and N. J. A. Sloane, Theory of Error-Correcting Codes, 1977, Chapter 19, Eq. (14), p. 601 and Theorem 3c, p. 602; also Problem 5 p. 620.

Index entries for sequences related to linear recurrences with constant coefficients

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 210

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 449

F. J. MacWilliams, C. L. Mallows and N. J. A. Sloane, Generalizations of Gleason's theorem on weight enumerators of self-dual codes, IEEE Trans. Inform. Theory, 18 (1972), 794-805; see p. 802, col. 2, foot.

G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.

Jan Snellman and Michael Paulsen, Enumeration of Concave Integer Partitions, J. Integer Seqs., Vol. 7, 2004.

Index entries for Molien series

G.f.: 1/((1-x)*(1-x^3)).

Convolution of A049347 and A000027. G.f. : 1/((1-x)^2(1+x+x^2)); a(n)=sum{k=0..n, (k+1)*2sqrt(3)cos(2*pi*(n-k)/3+pi/6)/3}. - Paul Barry (pbarry(AT)wit.ie), May 19 2004

The g.f. is 1/(1-V_trefoil(x)), where V_trefoil is the Jones polynomial of the trefoil knot. - Paul Barry (pbarry(AT)wit.ie), Oct 08 2004

floor(n/3)+1.

a(2n)=A004396(n+1) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 14 2006

Also, a(n)=Ceiling (n/3), n>=1. - Mohammad K. Azarian (azarian(AT)evansville.edu), May 22 2007

a(n)=(1/9)*Sum{k=0..n}{-2*(k mod 3)+[(k+1) mod 3]+4*[(k+2) mod 3]}, with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Nov 21 2008]

Table[Floor[n/3], {n, 0, 90}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 02 2006

(PARI) a(n)=n\3+1

Cf. A008621, A002264.

a(n)=A010766(n+3, 3).

Sequence in context: A032615 A086161 A002264 this_sequence A104581 A113675 A020912

Adjacent sequences: A008617 A008618 A008619 this_sequence A008621 A008622 A008623

nonn,easy,nice

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