cp's OEIS Frontend

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.

Showing 1-10 of 10 results.

A034188 Number of binary codes of length 3 with n words.

Original entry on oeis.org

1, 1, 3, 3, 6, 3, 3, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

References

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

Links

Crossrefs

Cf. A034189, A034190, A034191, A034192, A034193, A034194, A034195, A034196, A034197.
A row of A039754.

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

Original entry on oeis.org

1, 1, 4, 6, 19, 27, 50, 56, 74, 56, 50, 27, 19, 6, 4, 1, 1
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

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

Crossrefs

Cf. A034188, A034190, A034191, A034192, A034193, A034194, A034195, A034196, A034197.
Cf. A171872 and A171876. - Robert Munafo, Jan 25 2010
A row of A039754.

Programs

  • 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 *)

Extensions

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

A034190 Number of binary codes of length 5 with n words.

Original entry on oeis.org

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
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

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

Crossrefs

Row n=5 of A039754.
Cf. A034188, A034189, A034191, A034192, A034193, A034194, A034195, A034196, A034197.
Cf. A171872 and A171876. - Robert Munafo, Jan 25 2010

Programs

  • 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 *)

Extensions

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

A034191 Number of binary codes of length 6 with n words.

Original entry on oeis.org

1, 1, 6, 16, 103, 497, 3253, 19735, 120843, 681474, 3561696, 16938566, 73500514, 290751447, 1052201890, 3492397119, 10666911842, 30064448972, 78409442414, 189678764492, 426539774378, 893346071377, 1745593733454
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

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

Crossrefs

Row n=6 of A039754.
Cf. A034188, A034189, A034190, A034192, A034193, A034194, A034195, A034196, A034197.

Programs

  • 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 *)

Extensions

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

A034193 Number of binary codes of length 8 with n words.

Original entry on oeis.org

1, 1, 8, 32, 373, 4647, 91028, 2074059, 51107344, 1245930065, 28900653074, 625715497344, 12562875567065, 233750783834504, 4038807303045625, 65003434860142353, 977872935273906860, 13795944871933252078
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Row n=8 of A039754.
Cf. A034188, A034189, A034190, A034191, A034192, A034194, A034195, A034196, A034197.

A034194 Number of binary codes of length 9 with n words.

Original entry on oeis.org

1, 1, 9, 43, 649, 12320, 404154, 16957301, 805174011, 38921113842, 1816451773537, 79799396735243, 3267743403989063, 124448560749072651, 4413401558241969897, 146147123072487323183, 4533679418476771721737
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Row n=9 of A039754.
Cf. A034188, A034189, A034190, A034191, A034192, A034193, A034195, A034196, A034197.

A034195 Number of binary codes of length 10 with n words.

Original entry on oeis.org

1, 1, 10, 56, 1079, 30493, 1646000, 124727148, 11244522420, 1063289204514, 98630203059528, 8687099045170277, 716661691995997667, 55145074470990131334, 3958951571937696919325
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A034188, A034189, A034190, A034191, A034192, A034193, A034194, A034196, A034197.

A034196 Number of binary codes of length 11 with n words.

Original entry on oeis.org

1, 1, 11, 71, 1727, 71218, 6232542, 840130123, 142255064793, 26089682147964, 4776270743160543, 838032011887365999, 138409456269288832810, 21380210213948881081642, 3086290263475796210940632
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A034188, A034189, A034190, A034191, A034192, A034193, A034194, A034195, A034197.

A034197 Number of binary codes of length 12 with n words.

Original entry on oeis.org

1, 1, 12, 89, 2681, 158374, 22151853, 5244256701, 1653293013642, 584494025830394, 210237300968913438, 73212582945836596465, 24126483152959778734211, 7456837714994642537616273
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

Last term is a(2^12) = 1. - Sean A. Irvine, Aug 07 2020

Links

Crossrefs

Cf. A034188, A034189, A034190, A034191, A034192, A034193, A034194, A034195, A034196.

A034199 Number of binary codes (not necessarily linear) of length n with 4 words.

Original entry on oeis.org

0, 1, 6, 19, 47, 103, 203, 373, 649, 1079, 1727, 2681, 4048, 5969, 8620, 12218, 17028, 23378, 31654, 42324, 55941, 73155, 94725
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A034188, A034189, A034190, A034191, A034192, A034193, A034194, A034195, A034196, A034197, A034198.

Extensions

a(15)-a(23) from Sean A. Irvine, Aug 07 2020
Showing 1-10 of 10 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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