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

A268897 Number of n X n 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

0, 36, 1584, 118584, 17194680, 5344944120, 3679171151832, 5729028666080112, 20420870331077074152, 167959998252207918469944, 3205098856567970748329302728, 142456755446316393140675874983544
Offset: 1

Views

Author

R. H. Hardin, Feb 15 2016

Keywords

Comments

Diagonal of A268904.

Examples

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

Links

Crossrefs

Cf. A268904.

A268898 Number of n X 2 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

3, 36, 240, 1344, 6912, 33792, 159744, 737280, 3342336, 14942208, 66060288, 289406976, 1258291200, 5435817984, 23353884672, 99857989632, 425201762304, 1803886264320, 7627861917696, 32160715112448, 135239930216448
Offset: 1

Views

Author

R. H. Hardin, Feb 15 2016

Keywords

Examples

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

Links

Crossrefs

Column 2 of A268904.

Formula

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

A268899 Number of n X 3 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

12, 168, 1584, 12960, 98496, 715392, 5038848, 34712064, 235146240, 1572120576, 10400182272, 68205846528, 444063596544, 2873352683520, 18493942726656, 118486616113152, 756057455198208, 4807171282305024, 30467987000524800
Offset: 1

Views

Author

R. H. Hardin, Feb 15 2016

Keywords

Examples

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

Links

Crossrefs

Column 3 of A268904.

Formula

Empirical: a(n) = 12*a(n-1) - 36*a(n-2).
Conjectures from Colin Barker, Jan 16 2019: (Start)
G.f.: 12*x*(1 + 2*x) / (1 - 6*x)^2.
a(n) = 2^(n+1) * 3^(n-1) * (4*n-1).
(End)

A268900 Number of n X 4 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

36, 696, 9720, 118584, 1347192, 14644152, 154472184, 1594323000, 16185567096, 162200044728, 1608569870328, 15816054042936, 154394813276280, 1498006261495224, 14458132831535352, 138907883786523192
Offset: 1

Views

Author

R. H. Hardin, Feb 15 2016

Keywords

Examples

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

Links

Crossrefs

Column 4 of A268904.

Formula

Empirical: a(n) = 18*a(n-1) - 81*a(n-2) for n>3.
Conjectures from Colin Barker, Jan 16 2019: (Start)
G.f.: 12*x*(3 + 4*x + 9*x^2) / (1 - 9*x)^2.
a(n) = 8 * 3^(2*n-3) * (16*n-3) for n>1.
(End)

A268901 Number of n X 5 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

96, 2664, 54936, 1004184, 17194680, 282550680, 4513169016, 70609114584, 1087342615224, 16536864398616, 248976164499192, 3717450986032728, 55118358414612792, 812385229848253848, 11912420604393611640
Offset: 1

Views

Author

R. H. Hardin, Feb 15 2016

Keywords

Examples

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

Links

Crossrefs

Column 5 of A268904.

Formula

Empirical: a(n) = 30*a(n-1) - 261*a(n-2) + 540*a(n-3) - 324*a(n-4).
Empirical g.f.: 24*x*(4 - 9*x + 3*x^2 - 18*x^3) / (1 - 15*x + 18*x^2)^2. - Colin Barker, Jan 16 2019

A268902 Number of n X 6 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

240, 9720, 299088, 8250912, 214142760, 5344944120, 129834259704, 3091414865040, 72488795124312, 1679265104747616, 38520989302343760, 876481043382776664, 19806871824479466648, 444994736265664134120, 9947337685046673808176
Offset: 1

Views

Author

R. H. Hardin, Feb 15 2016

Keywords

Examples

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

Links

Crossrefs

Column 6 of A268904.

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*(10 - 95*x + 262*x^2 + 93*x^3 - 1485*x^4 + 1701*x^5) / (1 - 25*x + 90*x^2 - 81*x^3)^2. - Colin Barker, Jan 16 2019

A268903 Number of nX7 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

576, 34344, 1585800, 66210264, 2611960344, 99308573208, 3679171151832, 133712637011640, 4788143315276472, 169455769674019992, 5940079034652505944, 206577531186380751096, 7136252899974195705720, 245118805391945325271896
Offset: 1

Views

Author

R. H. Hardin, Feb 15 2016

Keywords

Comments

Column 7 of A268904.

Examples

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

Links

Crossrefs

Cf. A268904.

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)

A268905 Number of 2 X n 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

0, 36, 168, 696, 2664, 9720, 34344, 118584, 402408, 1347192, 4461480, 14644152, 47711592, 154472184, 497428776, 1594323000, 5089079016, 16185567096, 51311691432, 162200044728, 511395045480, 1608569870328, 5048863812648
Offset: 1

Views

Author

R. H. Hardin, Feb 15 2016

Keywords

Examples

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

Links

Crossrefs

Row 2 of A268904.

Formula

Empirical: a(n) = 6*a(n-1) - 9*a(n-2) for n>4.
Conjectures from Colin Barker, Jan 16 2019: (Start)
G.f.: 12*x^2*(3 - x)*(1 - x) / (1 - 3*x)^2.
a(n) = 8*3^(n-3) * (8*n-3) for n>2.
(End)

A268906 Number of 3 X n 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

0, 240, 1584, 9720, 54936, 299088, 1585800, 8244288, 42216696, 213602256, 1070280936, 5319700704, 26262038232, 128900271600, 629516497608, 3061019061504, 14827169463480, 71576870716944, 344483107968168
Offset: 1

Views

Author

R. H. Hardin, Feb 15 2016

Keywords

Examples

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

Links

Crossrefs

Row 3 of A268904.

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.: 24*x^2*(10 - 34*x + 35*x^2 - 47*x^3 + 37*x^4) / (1 - 5*x + 2*x^2)^2. - Colin Barker, Jan 16 2019

A268907 Number of 4Xn 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

0, 1344, 12960, 118584, 1004184, 8250912, 66210264, 522241560, 4063962024, 31282792704, 238663638432, 1807307152056, 13599932970888, 101786388133320, 758232651966984, 5625079743143376, 41579318178922608, 306353541215271960
Offset: 1

Views

Author

R. H. Hardin, Feb 15 2016

Keywords

Comments

Row 4 of A268904.

Examples

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

Links

Crossrefs

Cf. A268904.

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.

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