A034189 Number of binary codes of length 4 with n words.

1, 1, 4, 6, 19, 27, 50, 56, 74, 56, 50, 27, 19, 6, 4, 1, 1

Offset

0,3

Comments

Also number of 2-colorings of the vertices of the 4-cube having n nodes of one color.

References

W. Y. C. Chen, Induced cycle structures of the hyperoctahedral group. SIAM J. Disc. Math. 6 (1993), 353-362.

H. Fripertinger, Enumeration, construction and random generation of block codes, Designs, Codes, Crypt., 14 (1998), 213-219.

R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1979.

Links

Table of n, a(n) for n=0..16.

H. Fripertinger, Isometry Classes of Codes

Mathematica

(* From Robert A. Russell, May 08 2007: (Start) *)
P[ n_Integer ]:=P[ n ]=P[ n, n ]; P[ n_Integer, _ ]:={}/; (n<0); (* partitions *)
P[ 0, _ ]:={{}}; P[ n_Integer, 1 ]:={Table[ 1, {n} ]}; P[ _, 0 ]:={}; (*S.S. Skiena*)
P[ n_Integer, m_Integer ]:=Join[ Map[ (Prepend[ #, m ])&, P[ n-m, m ] ], P[ n, m-1 ] ];
AC[ d_Integer ]:=Module[ {C, M, p}, (* from W.Y.C. Chen algorithm *)
M[ p_List ]:=Plus@@p!/(Times@@p Times@@(Length/@Split[ p ]!));
C[ p_List, q_List ]:=Module[ {r, m, k, x}, r=If[ 0==Length[ q ], 1, 2 2^
IntegerExponent[ LCM@@q, 2 ] ]; m=LCM@@Join[ p/GCD[ r, p ], q/GCD[ r, q ] ];
CoefficientList[ Expand[ Product[ (1+x^(k r))^((Plus@@Map[ MoebiusMu[ k/# ]
2^Plus@@GCD[# r, Join[ p, q ] ]&, Divisors[ k ] ])/(k r)), {k, 1, m} ] ], x ] ];
Sum[ Binomial[ d, p ]Plus@@Plus@@Outer[ M[ #1 ]M[ #2 ]C[ #1, #2 ]2^(d-Length[ #1 ]-Length[ #2 ])&, P[ p ], P[ d-p ], 1 ], {p, 0, d} ]/(d!2^d) ]; AC[ 4 ]
(* End *)

Crossrefs

Cf. A034188, A034190, A034191, A034192, A034193, A034194, A034195, A034196, A034197.

Cf. A171872 and A171876. - Robert Munafo, Jan 25 2010

A row of A039754.

Sequence in context: A012928 A013160 A153777 * A024697 A024874 A095383

Adjacent sequences: A034186 A034187 A034188 * A034190 A034191 A034192

Keyword

nonn,fini,full

Author

N. J. A. Sloane

Extensions

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, May 11 2007

Status

approved