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A034191 Number of binary codes of length 6 with n words. 11
1, 1, 6, 16, 103, 497, 3253, 19735, 120843, 681474, 3561696, 16938566, 73500514, 290751447, 1052201890, 3492397119, 10666911842, 30064448972, 78409442414, 189678764492, 426539774378, 893346071377, 1745593733454 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Also number of 2-colorings of the vertices of the 6-cube having n nodes of one color.
The b-file shows the full sequence.
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[ 6 ]
(* End *)
CROSSREFS
Row n=6 of A039754.
Sequence in context: A229566 A222965 A009354 * A368875 A115331 A239027
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 March 29 03:51 EDT 2024. Contains 371264 sequences. (Running on oeis4.)