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A034190 Number of binary codes of length 5 with n words. 12
1, 1, 5, 10, 47, 131, 472, 1326, 3779, 9013, 19963, 38073, 65664, 98804, 133576, 158658, 169112, 158658, 133576, 98804, 65664, 38073, 19963, 9013, 3779, 1326, 472, 131, 47, 10, 5, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Also number of 2-colorings of the vertices of the 5-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
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[ 5 ]
(* End *)
CROSSREFS
Row n=5 of A039754.
Cf. A171872 and A171876. - Robert Munafo, Jan 25 2010
Sequence in context: A270085 A035406 A103932 * A216390 A305476 A270089
KEYWORD
nonn,fini,full
AUTHOR
EXTENSIONS
Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, May 11 2007
STATUS
approved

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Last modified May 19 14:45 EDT 2024. Contains 372698 sequences. (Running on oeis4.)