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 A034191 Number of binary codes of length 6 with n words. 10
 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 R. W. Robinson, Table of n, a(n) for n = 0..65 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 Cf. A034188, A034189, A034190, A034192, A034193, A034194, A034195, A034196, A034197. Sequence in context: A229566 A222965 A009354 * A115331 A239027 A218976 Adjacent sequences:  A034188 A034189 A034190 * A034192 A034193 A034194 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 December 16 09:34 EST 2018. Contains 318160 sequences. (Running on oeis4.)