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.

A233162 Number of n X 1 0..7 arrays with no element x(i,j) adjacent to itself or value 7-x(i,j) horizontally, diagonally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 3 4 5 and 6, 2 appearing before 3 4 and 5, and 3 appearing before 4 in row major order (unlabeled 8-colorings with no clashing color pairs).

Original entry on oeis.org

1, 1, 3, 11, 48, 236, 1248, 6896, 39168, 226496, 1325568, 7821056, 46399488, 276294656, 1649369088, 9862639616, 59041579008, 353712521216, 2120127479808, 12712174616576, 76238687305728, 457294683570176, 2743218342985728
Offset: 1

Views

Author

R. H. Hardin, Dec 05 2013

Keywords

Comments

Column 1 of A233168.

Examples

			Some solutions for n=5:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....1....1....1....1....1....1....1....1....1....1....1....1....1....1
..7....7....2....0....2....2....2....2....2....7....2....2....7....0....2....0
..6....2....6....2....6....7....1....7....7....1....6....0....2....1....6....2
..7....0....3....6....7....3....2....5....1....2....2....6....6....7....0....1

Links

Crossrefs

Cf. A233168.

Formula

Empirical: a(n) = 12*a(n-1) -44*a(n-2) +48*a(n-3) for n>4.
Conjectures from Colin Barker, Feb 18 2018: (Start)
G.f.: x*(1 - 11*x + 35*x^2 - 29*x^3) / ((1 - 2*x)*(1 - 4*x)*(1 - 6*x)).
a(n) = (2^(n-6)*(90 + 9*2^n + 2*3^n)) / 9 for n>1. (End)

A233161 Number of n X n 0..7 arrays with no element x(i,j) adjacent to itself or value 7-x(i,j) horizontally, diagonally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 3 4 5 and 6, 2 appearing before 3 4 and 5, and 3 appearing before 4 in row major order (unlabelled 8-colorings with no clashing color pairs).

Original entry on oeis.org

1, 1, 96, 28672, 31457280, 133143986176, 2216615441596416, 146421031085069565952, 38534510500216304943759360, 40485591044789076510300958621696
Offset: 1

Views

Author

R. H. Hardin, Dec 05 2013

Keywords

Comments

Diagonal of A233168

Examples

			Some solutions for n=4
..0..1..0..2....0..1..2..1....0..1..2..1....0..1..7..1....0..1..2..6
..3..5..3..6....5..3..7..3....5..3..0..3....2..3..5..3....5..3..0..4
..0..6..0..2....0..6..5..6....0..6..2..1....1..7..6..7....7..6..5..1
..4..2..3..6....2..4..7..3....5..3..0..4....4..5..3..5....5..4..7..3

Links

A233163 Number of n X 3 0..7 arrays with no element x(i,j) adjacent to itself or value 7-x(i,j) horizontally, diagonally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 3 4 5 and 6, 2 appearing before 3 4 and 5, and 3 appearing before 4 in row major order (unlabelled 8-colorings with no clashing color pairs).

Original entry on oeis.org

3, 8, 96, 1280, 18432, 278528, 4325376, 68157440, 1082130432, 17246978048, 275414777856, 4402341478400, 70403103916032, 1126174784749568, 18016597532737536, 288247968337756160, 4611826755915743232
Offset: 1

Views

Author

R. H. Hardin, Dec 05 2013

Keywords

Examples

			Some solutions for n=5:
..0..1..2....0..1..7....0..1..0....0..1..7....0..1..0....0..1..2....0..1..7
..5..3..7....2..3..2....2..3..5....2..3..2....2..3..2....5..3..7....2..3..2
..0..6..2....6..0..1....1..0..1....0..6..7....0..1..7....7..1..5....0..1..0
..5..4..0....3..2..3....3..5..4....4..5..3....3..5..4....2..4..7....4..2..3
..7..6..5....1..0..1....0..1..7....1..7..6....7..6..7....0..6..5....6..0..6

Links

Crossrefs

Column 3 of A233168.

Formula

Empirical: a(n) = 24*a(n-1) - 128*a(n-2) for n>3.
Conjectures from Colin Barker, Oct 09 2018: (Start)
G.f.: x*(3 - 64*x + 288*x^2) / ((1 - 8*x)*(1 - 16*x)).
a(n) = 8^(n-2) * (2^n+4) for n>1.
(End)

A233164 Number of n X 4 0..7 arrays with no element x(i,j) adjacent to itself or value 7-x(i,j) horizontally, diagonally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 3 4 5 and 6, 2 appearing before 3 4 and 5, and 3 appearing before 4 in row major order (unlabelled 8-colorings with no clashing color pairs).

Original entry on oeis.org

11, 64, 1280, 28672, 720896, 19922944, 587202560, 17985175552, 562640715776, 17798344474624, 566248488304640, 18067175067615232, 577305177233555456, 18460254872591663104, 590511983140819435520, 18892924695992401395712
Offset: 1

Views

Author

R. H. Hardin, Dec 05 2013

Keywords

Examples

			Some solutions for n=4:
..0..1..2..1....0..1..7..1....0..1..0..1....0..1..0..1....0..1..0..2
..5..3..0..4....2..3..2..4....2..3..2..4....2..3..5..4....3..2..4..1
..0..6..5..6....1..0..6..0....0..6..7..6....0..1..0..1....0..6..0..2
..5..3..7..4....5..4..2..4....5..3..2..3....5..4..5..4....3..5..3..6

Links

Crossrefs

Column 4 of A233168.

Formula

Empirical: a(n) = 48*a(n-1) - 512*a(n-2) for n>3.
Conjectures from Colin Barker, Oct 09 2018: (Start)
G.f.: x*(11 - 464*x + 3840*x^2) / ((1 - 16*x)*(1 - 32*x)).
a(n) = 4^(2*n-3) * (2^n+12) for n>1.
(End)

A233165 Number of n X 5 0..7 arrays with no element x(i,j) adjacent to itself or value 7-x(i,j) horizontally, diagonally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 3 4 5 and 6, 2 appearing before 3 4 and 5, and 3 appearing before 4 in row major order (unlabelled 8-colorings with no clashing color pairs).

Original entry on oeis.org

48, 512, 18432, 720896, 31457280, 1543503872, 83751862272, 4879082848256, 296868139499520, 18506979718725632, 1168684103302643712, 74291379453103702016, 4738507383934141071360, 302747963737721161121792
Offset: 1

Views

Author

R. H. Hardin, Dec 05 2013

Keywords

Examples

			Some solutions for n=3:
..0..1..7..2..7....0..1..7..6..2....0..1..2..3..2....0..1..2..1..2
..3..2..3..6..4....5..3..2..3..0....2..3..7..1..7....2..3..7..3..7
..0..6..7..2..0....0..6..7..6..5....7..6..2..3..5....0..6..5..1..2

Links

Crossrefs

Column 5 of A233168.

Formula

Empirical: a(n) = 96*a(n-1) - 2048*a(n-2) for n>3.
Conjectures from Colin Barker, Oct 09 2018: (Start)
G.f.: 16*x*(3 - 256*x + 4224*x^2) / ((1 - 32*x)*(1 - 64*x)).
a(n) = 2^(5*n-6) * (2^n+28) for n>1.
(End)

A233166 Number of n X 6 0..7 arrays with no element x(i,j) adjacent to itself or value 7-x(i,j) horizontally, diagonally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 3 4 5 and 6, 2 appearing before 3 4 and 5, and 3 appearing before 4 in row major order (unlabelled 8-colorings with no clashing color pairs).

Original entry on oeis.org

236, 4096, 278528, 19922944, 1543503872, 133143986176, 12919261626368, 1389782697508864, 161003686678495232, 19527607984278470656, 2430358531711233425408, 306658673481347586064384
Offset: 1

Views

Author

R. H. Hardin, Dec 05 2013

Keywords

Examples

			Some solutions for n=2:
..0..1..0..6..7..2....0..1..2..6..7..3....0..1..2..6..0..1....0..1..2..3..0..6
..3..5..4..2..4..6....2..4..7..4..2..1....5..3..0..4..2..4....2..3..0..1..2..4

Links

Crossrefs

Column 6 of A233168.

Formula

Empirical: a(n) = 192*a(n-1) - 8192*a(n-2) for n>3.
Conjectures from Colin Barker, Oct 09 2018: (Start)
G.f.: 4*x*(59 - 10304*x + 356352*x^2) / ((1 - 64*x)*(1 - 128*x)).
a(n) = 64^(n-1) * (2^n+60) for n>1.
(End)

A233167 Number of n X 7 0..7 arrays with no element x(i,j) adjacent to itself or value 7-x(i,j) horizontally, diagonally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 3 4 5 and 6, 2 appearing before 3 4 and 5, and 3 appearing before 4 in row major order (unlabeled 8-colorings with no clashing color pairs).

Original entry on oeis.org

1248, 32768, 4325376, 587202560, 83751862272, 12919261626368, 2216615441596416, 427841964600197120, 91657259616244334592, 21176862196618565255168, 5128490000396434702073856
Offset: 1

Views

Author

R. H. Hardin, Dec 05 2013

Keywords

Examples

			Some solutions for n=2:
..0..1..2..1..2..1..2....0..1..2..6..7..6..0....0..1..2..6..7..1..5
..2..3..0..3..0..4..0....5..3..7..4..2..3..5....5..3..7..3..2..4..7

Links

Crossrefs

Column 7 of A233168.

Formula

Empirical: a(n) = 384*a(n-1) - 32768*a(n-2) for n>3.
Conjectures from Colin Barker, Oct 09 2018: (Start)
G.f.: 32*x*(39 - 13952*x + 1019904*x^2) / ((1 - 128*x)*(1 - 256*x)).
a(n) = 2^(7*n-6) * (2^n+124) for n>1. (End)
Showing 1-7 of 7 results.

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

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