0,4

Also a(n+1) = number of distinct (infinite) output sequences from binary n-stage shift register which feeds back the complement of the sum of its contents. E.g. for n=5 there are 6 such sequences.

Also a(n+1) = number of binary vectors (x_1,...x_n) satisfying Sum_{i=1..n} i*x_i = 0 (mod n+1) = size of Varshamov-Tenengolts code VT_0(n). E.g. |VT_0(5)| = 6 = a(6).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

A. E. Brouwer, The Enumeration of Locally Transitive Tournaments. Math. Centr. Report ZW138, Amsterdam, 1980.

S. Butenko, P. Pardalos, I. Sergienko, V. P. Shylo and P. Stetsyuk, Estimating the size of correcting codes using extremal graph problems, in Optimization: Structure and Applications, edited by Charles Pearce, Kluwer, to appear, 2003.

B. D. Ginsburg, On a number theory function applicable in coding theory, Problemy Kibernetiki, No. 19 (1967), pp. 249-252.

S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967, p. 172.

R. W. Hall and P. Klingsberg, Asymmetric rhythms and tiling canons, Amer. Math. Monthly, 113 (2006), 887-896.

N. J. A. Sloane, On single-deletion-correcting codes, in Codes and Designs (Columbus, OH, 2000), 273-291, Ohio State Univ. Math. Res. Inst. Publ., 10, de Gruyter, Berlin, 2002.

T. D. Noe, Table of n, a(n) for n = 0..200

P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.

N. J. A. Sloane, On single-deletion-correcting codes

N. J. A. Sloane, Challenge Problems: Independent Sets in Graphs

Index entries for sequences related to tournaments

Index entries for sequences related to necklaces

Index entries for sequences related to subset sums modulo m

Sum {odd d divides n } (phi(d)*2^(n/d))/(2n), n>0.

For n=3 the 2 output sequences are 000111000111... and 010101...

For n=4 the 4 output sequences are those with periodic parts {0000011111, 0001011101, 0010011011, 01}.

with(numtheory); A000016 := proc(n) local d, t1; if n = 0 then RETURN(1) else t1 := 0; for d from 1 to n do if n mod d = 0 and d mod 2 = 1 then t1 := t1+phi(d)*2^(n/d)/(2*n); fi; od; RETURN(t1); fi; end;

(PARI) a(n)=if(n<1, n >= 0, sumdiv(n, k, (k%2)*eulerphi(k)*2^(n/k))/(2*n)).

Cf. A000048, A000031, A000013. The main diagonal of table A068009, the left edge of triangle A053633. Equals A063776(n)/2.

Sequence in context: A163733 A084202 A053637 this_sequence A060553 A032307 A007560

Adjacent sequences: A000013 A000014 A000015 this_sequence A000017 A000018 A000019

nonn,nice,easy

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

More terms from Michael Somos