A184271 -id:A184271 - cp's OEIS frontend

A184268 Number of distinct n X 6 toroidal binary arrays.

14, 362, 14624, 699600, 35792568, 1908897152, 104715443852, 5864063066500, 333599974922264, 19215358463836552, 1117984489446008100, 65588423376054708480, 3874762242361630560584, 230271584688657874664612, 13754889325393505198471808, 825293359523595646115953700

Offset: 1

R. H. Hardin, Jan 10 2011

nonn

Vaclav Kotesovec, Table of n, a(n) for n = 1..550
S. N. Ethier, Counting toroidal binary arrays, arXiv preprint arXiv:1301.2352, 2013 and J. Int. Seq. 16 (2013) #13.4.7 .

Column 6 of A184271.

with(numtheory):
a:= n-> add(add(phi(c)*phi(d) *2^(6*n/ilcm(c, d)),
        d=divisors(n)), c=[1,2,3,6])/(6*n):
seq(a(n), n=1..25);  # Alois P. Heinz, Aug 25 2012

a(n) ~ 64^n / (6*n). - Vaclav Kotesovec, Sep 04 2014

More terms from Alois P. Heinz, Aug 25 2012

A184269 Number of distinct n X 7 toroidal binary arrays.

Original entry on oeis.org

20, 1182, 99880, 9587580, 981706832, 104715443852, 11488774559744, 1286742755471400, 146402730743793240, 16865594582168158776, 1962541914958813595480, 230271584688553159320640, 27207473390887478569212080, 3233802551602631768613571584

Offset: 1

R. H. Hardin, Jan 10 2011

nonn

Vaclav Kotesovec, Table of n, a(n) for n = 1..470
S. N. Ethier, Counting toroidal binary arrays, arXiv preprint arXiv:1301.2352, 2013 and J. Int. Seq. 16 (2013) #13.4.7.

Column 7 of A184271.

with(numtheory):
a:= n-> add(add(phi(c)*phi(d) *2^(7*n/ilcm(c, d)),
        d=divisors(n)), c=[1,7])/(7*n):
seq(a(n), n=1..20);  # Alois P. Heinz, Aug 25 2012

a(n) ~ 128^n / (7*n). - Vaclav Kotesovec, Sep 04 2014

More terms from Alois P. Heinz, Aug 25 2012

A184270 Number of distinct n X 8 toroidal binary arrays.

Original entry on oeis.org

36, 4150, 699252, 134223976, 27487816992, 5864063066500, 1286742755471400, 288230376353050816, 65588423374144427520, 15111572745224096425720, 3516875111606393874082104, 825293359523595646117352176, 195023169265881489687952047216

Offset: 1

R. H. Hardin, Jan 10 2011

nonn

Vaclav Kotesovec, Table of n, a(n) for n = 1..410
S. N. Ethier, Counting toroidal binary arrays, arXiv preprint arXiv:1301.2352, 2013 and J. Int. Seq. 16 (2013) #13.4.7.

Column 8 of A184271.

with(numtheory):
a:= n-> add(add(phi(c)*phi(d) *2^(8*n/ilcm(c, d)),
        d=divisors(n)), c=[1,2,4,8])/(8*n):
seq(a(n), n=1..20);  # Alois P. Heinz, Aug 25 2012

a(n) ~ 2^(8*n-3) / n. - Vaclav Kotesovec, Sep 04 2014

More terms from Alois P. Heinz, Aug 25 2012

cp's OEIS Frontend

A184268 Number of distinct n X 6 toroidal binary arrays.

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A184269 Number of distinct n X 7 toroidal binary arrays.

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A184270 Number of distinct n X 8 toroidal binary arrays.

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Author

Keywords

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Crossrefs

Programs

Maple

Formula

Extensions