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 13 results. Next

A268964 Number of n X n 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

3, 60, 2016, 136080, 18852912, 5712070032, 3870355944960, 5963413766987592, 21098726553552173712, 172587783760354579099176, 3279749300107885644432555744, 145303202175464965696103410891992
Offset: 1

Views

Author

R. H. Hardin, Feb 16 2016

Keywords

Comments

Diagonal of A268971.

Examples

			Some solutions for n=4
..0..1..0..1. .1..0..0..1. .1..2..0..0. .2..1..2..2. .0..1..0..0
..0..1..0..0. .1..0..2..1. .1..0..1..2. .2..1..2..1. .2..1..1..0
..2..1..0..0. .1..2..2..1. .1..0..1..2. .2..2..2..1. .0..0..1..0
..2..1..1..0. .2..2..2..2. .1..0..1..0. .1..1..2..1. .0..0..1..0

Links

Crossrefs

Cf. A268971.

A268965 Number of n X 2 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

9, 60, 336, 1728, 8448, 39936, 184320, 835584, 3735552, 16515072, 72351744, 314572800, 1358954496, 5838471168, 24964497408, 106300440576, 450971566080, 1906965479424, 8040178778112, 33809982554112, 141836999983104
Offset: 1

Views

Author

R. H. Hardin, Feb 16 2016

Keywords

Examples

			Some solutions for n=4:
..0..0. .0..0. .0..1. .2..2. .1..2. .1..0. .2..2. .0..2. .2..1. .0..1
..0..2. .1..1. .0..0. .1..1. .2..0. .0..0. .2..1. .2..1. .0..2. .2..2
..2..2. .2..1. .2..2. .2..2. .0..1. .2..2. .2..1. .0..0. .1..2. .2..0
..1..0. .2..1. .2..2. .2..1. .2..1. .1..0. .2..2. .0..0. .2..2. .1..2

Links

Crossrefs

Column 2 of A268971.

Formula

Empirical: a(n) = 8*a(n-1) - 16*a(n-2).
Conjectures from Colin Barker, Jan 17 2019: (Start)
G.f.: 3*x*(3 - 4*x) / (1 - 4*x)^2.
a(n) = 4^(n-1) * (6*n+3).
(End)

A268966 Number of n X 3 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

24, 240, 2016, 15552, 114048, 808704, 5598720, 38071296, 255301632, 1693052928, 11125776384, 72559411200, 470184984576, 3030081011712, 19434312695808, 124128835928064, 789910774087680, 5010291195641856, 31686706480545792
Offset: 1

Views

Author

R. H. Hardin, Feb 16 2016

Keywords

Examples

			Some solutions for n=4:
..1..0..0. .0..1..2. .0..2..2. .2..2..2. .0..0..0. .1..2..1. .1..2..2
..1..1..2. .2..2..2. .1..2..2. .1..2..2. .0..1..0. .2..1..0. .0..1..0
..2..2..2. .1..2..2. .2..2..2. .1..0..1. .2..0..1. .0..0..1. .0..0..1
..2..2..2. .2..1..0. .2..2..2. .1..0..0. .1..0..1. .1..2..1. .0..0..0

Links

Crossrefs

Column 3 of A268971.

Formula

Empirical: a(n) = 12*a(n-1) - 36*a(n-2).
Conjectures from Colin Barker, Jan 17 2019: (Start)
G.f.: 24*x*(1 - 2*x) / (1 - 6*x)^2.
a(n) = 2^(n+2) * 3^(n-1) * (2*n+1).
(End)

A268967 Number of n X 4 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

60, 912, 11664, 136080, 1504656, 16061328, 167226768, 1709114256, 17218688400, 171498136464, 1692252695952, 16569199473552, 161173122151824, 1559011041375120, 15007175850454416, 143849270956794768
Offset: 1

Views

Author

R. H. Hardin, Feb 16 2016

Keywords

Examples

			Some solutions for n=4:
..1..0..0..0. .1..0..1..2. .2..1..0..1. .2..1..2..1. .2..1..2..1
..1..0..0..1. .0..0..1..2. .0..0..0..0. .2..1..2..2. .2..1..2..2
..0..1..2..0. .1..0..2..2. .1..2..1..2. .2..2..1..2. .0..0..1..2
..2..1..0..0. .0..1..2..1. .1..0..1..0. .1..0..1..1. .1..2..1..2

Links

Crossrefs

Column 4 of A268971.

Formula

Empirical: a(n) = 18*a(n-1) - 81*a(n-2) for n>3.
Conjectures from Colin Barker, Jan 17 2019: (Start)
G.f.: 12*x*(1 - x)*(5 - 9*x) / (1 - 9*x)^2.
a(n) = 16*3^(2*n-3) * (8*n+3) for n>1.
(End)

A268968 Number of n X 5 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

144, 3312, 63792, 1125360, 18852912, 305242992, 4823705520, 74858700528, 1145496747312, 17332683832944, 259866681636528, 3866483993274864, 57157824214772784, 840294622720295280, 12294351113071353264
Offset: 1

Views

Author

R. H. Hardin, Feb 16 2016

Keywords

Examples

			Some solutions for n=3:
..0..1..2..0..1. .0..2..2..2..1. .1..0..1..0..0. .0..2..1..0..1
..2..2..1..0..0. .2..2..1..0..0. .1..0..0..1..0. .1..0..1..2..2
..1..0..0..1..2. .1..0..0..0..1. .2..1..0..1..0. .1..2..2..1..0

Links

Crossrefs

Column 5 of A268971.

Formula

Empirical: a(n) = 30*a(n-1) - 261*a(n-2) + 540*a(n-3) - 324*a(n-4).
Empirical g.f.: 144*x*(1 - 7*x + 14*x^2 - 12*x^3) / (1 - 15*x + 18*x^2)^2. - Colin Barker, Jan 17 2019

A268969 Number of n X 6 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

336, 11664, 339480, 9093528, 231730344, 5712070032, 137497776840, 3251386055664, 75828095546544, 1748970953035272, 39976056137974824, 906854671261865016, 20440902679961179824, 458229741557275128024
Offset: 1

Views

Author

R. H. Hardin, Feb 16 2016

Keywords

Examples

			Some solutions for n=2:
..1..0..0..0..1..2. .1..2..2..0..1..2. .0..0..1..2..2..2. .1..0..1..0..0..0
..0..1..0..0..1..1. .1..2..1..2..2..2. .0..1..2..2..2..2. .1..0..0..0..0..0

Links

Crossrefs

Column 6 of A268971.

Formula

Empirical: a(n) = 50*a(n-1) - 805*a(n-2) + 4662*a(n-3) - 12150*a(n-4) + 14580*a(n- 5) -6561*a(n-6).
Empirical g.f.: 24*x*(14 - 214*x + 1115*x^2 - 2391*x^3 + 1674*x^4 + 243*x^5) / (1 - 25*x + 90*x^2 - 81*x^3)^2. - Colin Barker, Jan 17 2019

A268970 Number of nX7 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

768, 40176, 1770048, 72081792, 2799406656, 105294777120, 3870355944960, 139818682627488, 4983158127443904, 175684152567641184, 6139001133769997952, 212930705454132284064, 7339160588604264574272, 251599271436625798745568
Offset: 1

Views

Author

R. H. Hardin, Feb 16 2016

Keywords

Comments

Column 7 of A268971.

Examples

			Some solutions for n=2
..2..2..1..0..1..2..2. .1..2..0..1..0..0..0. .0..1..2..1..0..1..0
..1..0..1..2..1..2..0. .2..1..0..0..0..0..0. .2..1..2..1..2..0..1

Links

Crossrefs

Cf. A268971.

Formula

Empirical: a(n) = 84*a(n-1) -2466*a(n-2) +31428*a(n-3) -206469*a(n-4) +750384*a(n-5) -1513404*a(n-6) +1574640*a(n-7) -656100*a(n-8)

A268972 Number of 2 X n 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

9, 60, 240, 912, 3312, 11664, 40176, 136080, 454896, 1504656, 4933872, 16061328, 51963120, 167226768, 535692528, 1709114256, 5433452784, 17218688400, 54411055344, 171498136464, 539289320688, 1692252695952, 5299912289520
Offset: 1

Views

Author

R. H. Hardin, Feb 16 2016

Keywords

Examples

			Some solutions for n=4:
..0..1..0..1. .2..2..1..2. .1..2..1..0. .2..1..0..0. .1..1..2..2
..0..0..0..2. .2..2..2..2. .2..2..1..0. .2..1..2..2. .2..2..2..1

Links

Crossrefs

Row 2 of A268971.

Formula

Empirical: a(n) = 6*a(n-1) - 9*a(n-2) for n>4.
Conjectures from Colin Barker, Jan 17 2019: (Start)
G.f.: 3*x*(3 - x)*(1 + x - 4*x^2) / (1 - 3*x)^2.
a(n) = 16*3^(n-3) * (4*n+3) for n>2.
(End)

A268973 Number of 3 X n 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

27, 336, 2016, 11664, 63792, 339480, 1770048, 9084744, 46050480, 231090264, 1150053408, 5683587048, 27921925008, 136471932792, 664055030016, 3218568401160, 15545839096944, 74855120204952, 359437016141280
Offset: 1

Views

Author

R. H. Hardin, Feb 16 2016

Keywords

Examples

			Some solutions for n=4:
..1..2..1..0. .2..2..2..2. .1..2..2..2. .2..1..2..2. .0..1..2..2
..1..2..0..1. .2..2..1..0. .1..2..2..1. .0..0..1..2. .0..1..2..1
..1..0..0..0. .1..2..1..2. .0..1..0..0. .1..2..1..0. .0..1..2..1

Links

Crossrefs

Row 3 of A268971.

Formula

Empirical: a(n) = 10*a(n-1) - 29*a(n-2) + 20*a(n-3) - 4*a(n-4) for n>6.
Empirical g.f.: 3*x*(9 + 22*x - 187*x^2 + 236*x^3 - 332*x^4 + 280*x^5) / (1 - 5*x + 2*x^2)^2. - Colin Barker, Jan 17 2019

A268974 Number of 4Xn 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

81, 1728, 15552, 136080, 1125360, 9093528, 72081792, 563173128, 4349328912, 33272350344, 252534743280, 1904015932416, 14274182767248, 106487231224248, 791006745522096, 5853579437553624, 43172409083833728, 317460508504648992
Offset: 1

Views

Author

R. H. Hardin, Feb 16 2016

Keywords

Comments

Row 4 of A268971.

Examples

			Some solutions for n=4
..2..1..0..0. .0..0..1..2. .0..1..0..0. .2..1..0..0. .0..1..2..1
..0..0..1..2. .0..2..1..2. .0..0..0..0. .0..0..0..0. .2..1..0..0
..1..2..2..2. .1..0..1..0. .2..1..0..0. .1..0..1..1. .0..0..1..2
..2..1..0..0. .0..0..0..0. .2..1..0..1. .1..0..0..0. .1..0..0..0

Links

Crossrefs

Cf. A268971.

Formula

Empirical: a(n) = 18*a(n-1) -111*a(n-2) +282*a(n-3) -333*a(n-4) +180*a(n-5) -36*a(n-6) for n>12
Showing 1-10 of 13 results. Next

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

Content is available under The OEIS End-User License Agreement.