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 1-7 of 7 results.

A183766 1/32 the number of (2n+1) X 4 binary arrays with equal numbers of 2 X 2 subblocks with sum mod two being 0 and 1.

Original entry on oeis.org

40, 7392, 1555840, 346131968, 79420170240, 18585877094400, 4409408507412480, 1056689477487820800, 255189244398549336064, 62004700939478066266112, 15140238779254079729172480, 3712064235466595220724908032
Offset: 1

Views

Author

R. H. Hardin, Jan 06 2011

Keywords

Comments

Column 3 of A183772(2n).

Examples

			Some solutions for 3 X 4:
..1..0..1..0....0..0..0..0....0..1..1..1....0..0..0..1....1..0..0..1
..0..1..1..0....0..1..1..0....0..1..0..1....1..0..1..0....0..0..1..0
..0..1..0..0....0..1..0..1....0..1..1..0....1..1..0..1....1..1..1..0

Links

A183767 1/32 the number of (n+1) X 5 binary arrays with equal numbers of 2 X 2 subblocks with sum mod two being 0 and 1.

Original entry on oeis.org

12, 280, 7392, 205920, 5912192, 173065984, 5134924800, 153876579840, 4646469273600, 141154845511680, 4309194677698560, 132086184685977600, 4062564621910867968, 125316146802859048960, 3875293808717379141632
Offset: 1

Views

Author

R. H. Hardin, Jan 06 2011

Keywords

Examples

			Some solutions for 3 X 5:
..0..0..1..1..0....0..0..0..1..1....1..0..1..1..1....0..0..0..1..1
..0..0..0..0..0....1..1..1..1..1....1..1..0..0..1....0..1..1..1..0
..0..0..0..1..0....0..1..0..0..1....1..1..1..1..1....0..0..0..0..1

Links

Crossrefs

Column 4 of A183772.

Formula

Empirically a(n) = 2^(3*n)*Gamma(2*n+1/2)/(Gamma(n+1/2)*n!). - Peter Luschny, Sep 24 2018
Conjectures from Peter Bala, Mar 11 2025: (Start)
1) a(n) = 2^n * binomial(4*n, 2*n).
2) a(n) = (4/3) * [x^n] T(3*n, 1 + x), where T(n, x) denotes the n-th Chebyshev polynomial of the first kind. (End)

A183768 1/32 the number of (2n+1) X 6 binary arrays with equal numbers of 2 X 2 subblocks with sum mod two being 0 and 1.

Original entry on oeis.org

2016, 5912192, 19855042560, 70577422755840, 258888921984516096, 968823452179344785408, 3676119951496408119115776, 14091184863095839321177456640, 54435471052008802940182132162560
Offset: 1

Views

Author

R. H. Hardin, Jan 06 2011

Keywords

Comments

Column 5 of A183772(2n).

Examples

			Some solutions for 3 X 6:
..0..0..0..1..0..1....0..1..1..1..1..1....1..1..0..0..0..1....1..0..0..0..1..0
..0..1..1..1..0..1....0..1..0..1..0..0....1..1..1..1..0..1....0..1..1..1..1..1
..1..1..1..0..0..1....0..0..1..0..0..0....0..0..1..0..1..1....0..0..0..0..1..0

Links

A183769 1/32 the number of (n+1) X 7 binary arrays with equal numbers of 2 X 2 subblocks with sum mod two being 0 and 1.

Original entry on oeis.org

160, 14784, 1555840, 173065984, 19855042560, 2323234636800, 275588031713280, 33021546171494400, 3987331943727333376, 484411726089672392704, 59141557731461248942080, 7250125459895693790478336
Offset: 1

Views

Author

R. H. Hardin, Jan 06 2011

Keywords

Comments

Column 6 of A183772.

Examples

			Some solutions for 3 X 7:
..0..0..0..1..0..0..1....0..0..0..0..0..1..0....0..0..0..0..1..1..0
..0..1..1..0..0..1..1....0..0..1..0..0..0..1....1..1..0..1..1..0..1
..0..0..0..1..1..1..1....1..0..1..1..0..0..1....1..1..0..0..0..1..1

Links

A183770 1/32 the number of (2n+1) X 8 binary arrays with equal numbers of 2 X 2 subblocks with sum mod two being 0 and 1.

Original entry on oeis.org

109824, 5134924800, 275588031713280, 15664518350357381120, 919029987874102029778944, 55014538812191247245224181760, 3339401594009138875954682737459200
Offset: 1

Views

Author

R. H. Hardin, Jan 06 2011

Keywords

Comments

Column 7 of A183772(2n).

Examples

			Some solutions for 3 X 8:
..0..0..0..0..0..1..0..0....0..0..0..0..0..1..0..1....0..0..0..0..0..0..1..1
..1..0..1..0..0..1..0..1....0..0..0..0..0..0..0..0....1..0..1..1..0..1..1..1
..1..0..1..0..1..0..0..0....1..0..1..1..1..0..1..1....0..1..1..1..0..1..1..0

Links

A183771 1/32 the number of (n+1) X 9 binary arrays with equal numbers of 2 X 2 subblocks with sum mod two being 0 and 1.

Original entry on oeis.org

2240, 823680, 346131968, 153876579840, 70577422755840, 33021546171494400, 15664518350357381120, 7506428481300850827264, 3625062729947846895239168, 1761398107886979915147182080, 860111024347049203759900262400
Offset: 1

Views

Author

R. H. Hardin, Jan 06 2011

Keywords

Comments

Column 8 of A183772.

Examples

			Some solutions for 3 X 9:
..0..0..0..0..0..0..0..0..0....0..0..0..0..0..0..0..0..1
..0..0..1..1..0..0..0..1..0....0..1..1..1..1..0..0..1..0
..0..1..0..1..1..1..0..1..0....1..0..1..0..1..0..0..0..0

Links

A183765 1/32 the number of (2n+1) X (2n+1) binary arrays with equal numbers of 2 X 2 subblocks with sum mod two being 0 and 1.

Original entry on oeis.org

6, 205920, 2323234636800, 7506428481300850827264, 6612015156138094974390271820169216
Offset: 1

Views

Author

R. H. Hardin, Jan 06 2011

Keywords

Comments

Diagonal A183772(2n,2n).

Examples

			Some solutions for 3 X 3:
..0..0..1....1..1..1....1..1..0....0..0..0....0..0..0....1..0..1....0..0..0
..1..1..0....0..1..1....0..1..1....0..1..0....1..1..0....1..1..0....0..0..0
..1..0..0....1..0..1....0..1..1....1..0..1....1..0..1....1..1..1....0..1..0
Showing 1-7 of 7 results.

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