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 11 results. Next

A184461 Half the number of (n+1) X 4 binary arrays with equal numbers of majority one 2 X 2 subblocks and majority zero 2 X 2 subblocks.

Original entry on oeis.org

26, 244, 3090, 42874, 616534, 9016218, 133687638, 2002023718, 30215911640, 458822048550, 7001737409868, 107286031628502, 1649589497350886, 25437988001627234, 393268526198504728, 6093317202558667778
Offset: 1

Views

Author

R. H. Hardin, Jan 15 2011

Keywords

Comments

Column 3 of A184467.

Examples

			Some solutions for 3 X 4
..0..1..1..1....0..1..1..1....0..0..1..0....0..0..1..1....0..0..1..0
..0..0..0..1....1..0..0..1....1..1..1..0....1..0..1..0....0..1..0..1
..0..1..1..1....1..1..0..0....0..0..0..0....1..1..0..0....1..0..1..1
...
...M..E..P.......E..E..P.......E..P..E.......M..E..P.......M..E..E...
...M..E..P.......P..M..M.......E..E..M.......P..E..M.......E..E..P...

Links

Crossrefs

Cf. A184467.

A184462 Half the number of (n+1) X 5 binary arrays with equal numbers of majority one 2 X 2 subblocks and majority zero 2 X 2 subblocks.

Original entry on oeis.org

91, 1693, 42874, 1181303, 33787978, 986306398, 29202473260, 873679701315, 26348265181700, 799618906955872, 24390561043319626, 747104810403124190, 22965144760897452728, 708038892975800125716, 21885932074900784746650
Offset: 1

Views

Author

R. H. Hardin, Jan 15 2011

Keywords

Comments

Column 4 of A184467.

Examples

			Some solutions for 3 X 5:
..0..1..0..0..0....0..1..1..0..0....0..0..0..0..0....0..0..0..1..0
..0..1..1..0..1....1..1..0..1..0....1..0..1..1..0....0..0..1..1..1
..0..1..1..0..1....0..0..0..1..0....1..1..1..0..1....0..0..0..1..1
...
...E..P..M..M.......P..P..E..M.......M..M..E..M.......M..M..P..P...
...E..P..E..E.......E..M..E..E.......P..P..P..E.......M..M..P..P...

Links

A184463 Half the number of (n+1)X6 binary arrays with equal numbers of majority one 2X2 subblocks and majority zero 2X2 subblocks.

Original entry on oeis.org

334, 12324, 616534, 33787978, 1925704384, 112210745828, 6636592203096, 396770571117114, 23916105558978568, 1450886078150900726, 88476176169893590874, 5418407297450835597284, 333018547198651616447064
Offset: 1

Views

Author

R. H. Hardin Jan 15 2011

Keywords

Comments

Column 5 of A184467

Examples

			Some solutions for 3X6
..0..1..0..0..0..1....0..1..1..1..1..1....0..0..1..1..1..0....0..1..1..0..1..0
..0..0..1..1..0..1....1..1..0..0..0..0....1..1..0..0..0..1....0..1..1..0..0..0
..0..1..1..1..1..0....1..1..0..0..1..0....1..1..0..0..1..1....1..0..1..1..1..0
...
...M..E..E..M..E.......P..P..E..E..E.......E..E..E..E..E.......E..P..E..M..M...
...M..P..P..P..E.......P..E..M..M..M.......P..E..M..M..P.......E..P..P..E..M...

Links

A184464 Half the number of (n+1)X7 binary arrays with equal numbers of majority one 2X2 subblocks and majority zero 2X2 subblocks.

Original entry on oeis.org

1212, 89908, 9016218, 986306398, 112210745828, 13061240432092, 1543735290815166, 184478487695574108, 22229843879368216722, 2696248965558609295818, 328747622872812708911124
Offset: 1

Views

Author

R. H. Hardin Jan 15 2011

Keywords

Comments

Column 6 of A184467

Examples

			Some solutions for 3X7
..0..1..1..1..0..0..0....0..0..0..0..0..0..1....0..1..1..1..0..0..0
..1..0..0..1..1..1..1....1..1..0..1..1..1..0....0..0..1..0..0..1..1
..1..0..0..0..0..0..0....0..0..1..0..1..1..0....1..0..1..1..1..0..1
...
...E..E..P..P..E..E.......E..M..M..E..E..E.......M..P..P..M..M..E...
...E..M..M..E..E..E.......E..E..E..P..P..E.......M..E..P..E..E..P...

Links

A184465 Half the number of (n+1) X 8 binary arrays with equal numbers of majority one 2 X 2 subblocks and majority zero 2 X 2 subblocks.

Original entry on oeis.org

4496, 667600, 133687638, 29202473260, 6636592203096, 1543735290815166, 364710845961492808, 87131390011496951676, 20992313186787145920488, 5091049499273022700839604, 1241234020860425300419060324
Offset: 1

Views

Author

R. H. Hardin, Jan 15 2011

Keywords

Comments

Column 7 of A184467.

Examples

			Some solutions for 3 X 8
..0..0..0..1..1..1..1..1....0..0..0..1..1..1..1..1....0..0..1..0..1..1..1..1
..0..0..1..0..1..1..0..1....0..0..0..0..1..1..1..1....1..0..0..1..0..1..1..1
..1..0..0..0..0..1..1..0....1..0..0..1..0..0..1..0....0..0..1..0..0..1..0..1
...
...M..M..E..P..P..P..P.......M..M..M..P..P..P..P.......M..M..E..E..P..P..P...
...M..M..M..M..P..P..E.......M..M..M..E..E..P..P.......M..M..E..M..E..P..P...

Links

Crossrefs

Cf. A184467.

A184466 Half the number of (n+1)X9 binary arrays with equal numbers of majority one 2X2 subblocks and majority zero 2X2 subblocks.

Original entry on oeis.org

16809, 5002165, 2002023718, 873679701315, 396770571117114, 184478487695574108, 87131390011496951676, 41619801566809753837565, 20050042433422012129360190, 9723279387982947487498511078
Offset: 1

Views

Author

R. H. Hardin Jan 15 2011

Keywords

Comments

Column 8 of A184467

Examples

			Some solutions for 3X9
..0..0..1..1..1..1..1..0..0....0..0..1..1..0..1..1..1..0
..0..0..0..1..0..0..1..1..1....0..0..0..1..0..0..1..1..0
..0..0..1..1..0..0..0..0..1....0..0..0..1..1..1..0..1..0
...
...M..M..P..P..E..P..P..E.......M..M..P..E..M..P..P..E...
...M..M..P..E..M..M..E..P.......M..M..E..P..E..E..P..E...

Links

A184459 Half the number of (n+1)X2 binary arrays with equal numbers of majority one 2X2 subblocks and majority zero 2X2 subblocks.

Original entry on oeis.org

3, 7, 26, 91, 334, 1212, 4496, 16809, 63442, 240728, 918208, 3516450, 13515164, 52099024, 201356496, 779967713, 3027239338, 11769964920, 45833102224, 178726147558, 697817190692, 2727647007504, 10672911447056, 41801025679450
Offset: 1

Views

Author

R. H. Hardin Jan 15 2011

Keywords

Comments

Column 1 of A184467

Examples

			All solutions for 3X2
..0..0....0..0....0..0....0..1....0..1....0..1....0..1
..1..1....0..1....1..0....1..0....1..0....0..1....0..1
..0..0....1..1....1..1....1..0....0..1....1..0....0..1
...
...E.......M.......M.......E.......E.......E.......E...
...E.......P.......P.......E.......E.......E.......E...

Links

A184460 Half the number of (n+1) X 3 binary arrays with equal numbers of majority one 2 X 2 subblocks and majority zero 2 X 2 subblocks.

Original entry on oeis.org

7, 35, 244, 1693, 12324, 89908, 667600, 5002165, 37777626, 286971238, 2190689600, 16790412468, 129127710164, 995937115474, 7700689112570, 59672216385587, 463283019198236, 3602944011508868, 28062509230063226, 218870000234417062
Offset: 1

Views

Author

R. H. Hardin, Jan 15 2011

Keywords

Comments

Column 2 of A184467.

Examples

			Some solutions for 5 X 3
..0..1..1....0..0..1....0..0..0....0..1..1....0..0..0....0..1..1....0..0..0
..0..1..1....0..1..0....1..1..0....0..1..0....0..1..1....0..0..0....0..1..0
..0..1..1....1..1..0....1..0..0....0..0..0....1..0..1....1..1..1....1..0..1
..0..0..0....0..1..0....1..1..1....1..1..1....0..0..1....0..1..0....1..1..0
..0..1..1....0..0..1....0..0..0....1..0..0....1..1..1....0..0..1....1..1..0
...
...E..P.......M..E.......E..M.......E..P.......M..E.......M..E.......M..M...
...E..P.......P..E.......P..M.......M..M.......E..P.......E..E.......E..E...
...M..E.......P..E.......P..E.......E..E.......M..E.......P..P.......P..E...
...M..E.......M..E.......E..E.......P..E.......E..P.......M..E.......P..E...

Links

Crossrefs

Cf. A184467.

A194467 Numbers m such that Sum_{k=1..m} ( - ) < 0, where r=sqrt(3) and c=sqrt(1/3), and < > denotes fractional part.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74
Offset: 1

Views

Author

Clark Kimberling, Aug 24 2011

Keywords

Comments

See A194368.

Crossrefs

Cf. A194368.

Programs

  • Mathematica
    Remove["Global`*"];
r = Sqrt[3]; c = 1/r;
x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 200}];
Flatten[Position[t1, 1]]    (* A184467 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 900}];
Flatten[Position[t3, 1]]    (* A184468 *)

A194468 Numbers m such that Sum_{k=1..m} ( - ) > 0, where r=sqrt(3) and c=sqrt(1/3), and < > denotes fractional part.

Original entry on oeis.org

7, 11, 14, 26, 52, 97, 104, 108, 111, 123, 149, 153, 156, 160, 163, 164, 165, 167, 175, 179, 182, 194, 201, 205, 208, 220, 317, 362, 369, 373, 376, 388, 414, 582, 679, 724, 731, 735, 738, 750, 776
Offset: 1

Views

Author

Clark Kimberling, Aug 24 2011

Keywords

Comments

See A194368.

Crossrefs

Cf. A194368.

Programs

  • Mathematica
    Remove["Global`*"];
r = Sqrt[3]; c = 1/r;
x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 200}];
Flatten[Position[t1, 1]]    (* A184467 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 900}];
Flatten[Position[t3, 1]]    (* A184468 *)
Showing 1-10 of 11 results. Next

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

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