This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A034190 #31 Jul 22 2022 16:43:21
%S A034190 1,1,5,10,47,131,472,1326,3779,9013,19963,38073,65664,98804,133576,
%T A034190 158658,169112,158658,133576,98804,65664,38073,19963,9013,3779,1326,
%U A034190 472,131,47,10,5,1,1
%N A034190 Number of binary codes of length 5 with n words.
%C A034190 Also number of 2-colorings of the vertices of the 5-cube having n nodes of one color.
%D A034190 W. Y. C. Chen, Induced cycle structures of the hyperoctahedral group. SIAM J. Disc. Math. 6 (1993), 353-362.
%D A034190 H. Fripertinger, Enumeration, construction and random generation of block codes, Designs, Codes, Crypt., 14 (1998), 213-219.
%D A034190 R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1979.
%H A034190 H. Fripertinger, <a href="http://www.mathe2.uni-bayreuth.de/frib/codes/tables.html">Isometry Classes of Codes</a>
%t A034190 (* From _Robert A. Russell_, May 08 2007: (Start) *)
%t A034190 P[ n_Integer ]:=P[ n ]=P[ n,n ];P[ n_Integer,_ ]:={}/;(n<0);(* partitions *)
%t A034190 P[ 0,_ ]:={{}};P[ n_Integer,1 ]:={Table[ 1,{n} ]};P[ _,0 ]:={};(*S.S. Skiena*)
%t A034190 P[ n_Integer,m_Integer ]:=Join[ Map[ (Prepend[ #,m ])&,P[ n-m,m ] ],P[ n,m-1 ] ];
%t A034190 AC[ d_Integer ]:=Module[ {C,M,p}, (* from W.Y.C. Chen algorithm *)
%t A034190 M[ p_List ]:=Plus@@p!/(Times@@p Times@@(Length/@Split[ p ]!));
%t A034190 C[ p_List,q_List ]:=Module[ {r,m,k,x},r=If[ 0==Length[ q ],1,2 2^
%t A034190 IntegerExponent[ LCM@@q,2 ] ];m=LCM@@Join[ p/GCD[ r,p ],q/GCD[ r,q ] ];
%t A034190 CoefficientList[ Expand[ Product[ (1+x^(k r))^((Plus@@Map[ MoebiusMu[ k/# ]
%t A034190 2^Plus@@GCD[# r,Join[ p,q ] ]&,Divisors[ k ] ])/(k r)),{k,1,m} ] ],x ] ];
%t A034190 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 ]
%t A034190 (* End *)
%Y A034190 Row n=5 of A039754.
%Y A034190 Cf. A034188, A034189, A034191, A034192, A034193, A034194, A034195, A034196, A034197.
%Y A034190 Cf. A171872 and A171876. - _Robert Munafo_, Jan 25 2010
%K A034190 nonn,fini,full
%O A034190 0,3
%A A034190 _N. J. A. Sloane_
%E A034190 Edited by _N. J. A. Sloane_ at the suggestion of _Andrew S. Plewe_, May 11 2007