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 12 results. Next

A233250 Number of n X n 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).

Original entry on oeis.org

1, 10, 4672, 23896064, 1159192379392, 525597937107992576, 2242238966451009797226496, 90075874398562137894702244954112, 34144912055691090021767126315871433129984
Offset: 1

Views

Author

R. H. Hardin, Dec 06 2013

Keywords

Comments

Diagonal of A233256

Examples

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

Links

A233251 Number of n X 3 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).

Original entry on oeis.org

3, 104, 4672, 221696, 10620928, 509640704, 24461443072, 1174138781696, 56358577635328, 2705211055407104, 129850125290831872, 6232805971010256896, 299174686264894947328, 14360384937966178402304, 689298477000386330755072
Offset: 1

Views

Author

R. H. Hardin, Dec 06 2013

Keywords

Examples

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

Links

Crossrefs

Column 3 of A233256.

Formula

Empirical: a(n) = 56*a(n-1) - 384*a(n-2).
Conjectures from Colin Barker, Oct 10 2018: (Start)
G.f.: x*(3 - 64*x) / ((1 - 8*x)*(1 - 48*x)).
a(n) = 8^(n-1) * (6^n+3) / 3.
(End)

A233252 Number of n X 4 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).

Original entry on oeis.org

10, 1184, 166400, 23896064, 3439984640, 495341010944, 71328837140480, 10271348253261824, 1479074079750225920, 212986666384520904704, 30670079941778824232960, 4416491511334675712835584
Offset: 1

Views

Author

R. H. Hardin, Dec 06 2013

Keywords

Examples

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

Links

Crossrefs

Column 4 of A233256.

Formula

Empirical: a(n) = 160*a(n-1) - 2304*a(n-2).
Conjectures from Colin Barker, Oct 10 2018: (Start)
G.f.: 2*x*(5 - 208*x) / ((1 - 16*x)*(1 - 144*x)).
a(n) = 2^(4*n-3) * (4*9^n+9) / 9.
(End)

A233253 Number of n X 5 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).

Original entry on oeis.org

36, 13952, 6049792, 2647261184, 1159192379392, 507618560835584, 222290692443996160, 97343107609552486400, 42627429627049642295296, 18666938062087506825838592, 8174421486934238668125110272
Offset: 1

Views

Author

R. H. Hardin, Dec 06 2013

Keywords

Examples

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

Links

Crossrefs

Column 5 of A233256.

Formula

Empirical: a(n) = 512*a(n-1) - 33792*a(n-2) + 589824*a(n-3).
Empirical g.f.: 4*x*(9 - 1120*x + 30720*x^2) / ((1 - 32*x)*(1 - 480*x + 18432*x^2)). - Colin Barker, Oct 11 2018

A233254 Number of n X 6 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).

Original entry on oeis.org

136, 166400, 220626944, 294517735424, 393427728465920, 525597937107992576, 702177183940808278016, 938080982436565861007360, 1253239344772433062871957504, 1674278572660580852636051308544
Offset: 1

Views

Author

R. H. Hardin, Dec 06 2013

Keywords

Examples

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

Links

Crossrefs

Column 6 of A233256.

Formula

Empirical: a(n) = 1664*a(n-1) - 471040*a(n-2) + 44826624*a(n-3) - 1358954496*a(n-4).
Empirical g.f.: 8*x*(17 - 7488*x + 974848*x^2 - 40108032*x^3) / ((1 - 64*x)*(1 - 1600*x + 368640*x^2 - 21233664*x^3)). - Colin Barker, Oct 11 2018

A233255 Number of n X 7 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabeled 6-colorings with no clashing color pairs).

Original entry on oeis.org

528, 1992704, 8050180096, 32835998056448, 134179300927602688, 548491734506604068864, 2242238966451009797226496, 9166394920089108387649814528, 37472795110784044637628292661248
Offset: 1

Views

Author

R. H. Hardin, Dec 06 2013

Keywords

Comments

Column 7 of A233256.

Examples

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

Links

Crossrefs

Cf. A233256.

Formula

Empirical: a(n) = 5504*a(n-1) -6438912*a(n-2) +2774532096*a(n-3) -478351982592*a(n-4) +27831388078080*a(n-5).

A233257 Number of 2 X n 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).

Original entry on oeis.org

3, 10, 104, 1184, 13952, 166400, 1992704, 23896064, 286687232, 3439984640, 41278767104, 495341010944, 5944075354112, 71328837140480, 855945777250304, 10271348253261824, 123256174744174592, 1479074079750225920
Offset: 1

Views

Author

R. H. Hardin, Dec 06 2013

Keywords

Examples

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

Links

Crossrefs

Row 2 of A233256.

Formula

Empirical: a(n) = 16*a(n-1) - 48*a(n-2) for n>3.
Conjectures from Colin Barker, Oct 11 2018: (Start)
G.f.: x*(3 - 38*x + 88*x^2) / ((1 - 4*x)*(1 - 12*x)).
a(n) = 2^(2*n-3) * (4*3^n+9) / 9 for n>1.
(End)

A233258 Number of 3 X n 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).

Original entry on oeis.org

11, 136, 4672, 166400, 6049792, 220626944, 8050180096, 293762760704, 10720053821440, 391200251052032, 14275841005453312, 520959990903603200, 19011091850007150592, 693760794065113186304, 25317011997007519154176
Offset: 1

Views

Author

R. H. Hardin, Dec 06 2013

Keywords

Examples

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

Links

Crossrefs

Row 3 of A233256.

Formula

Empirical: a(n) = 48*a(n-1) - 448*a(n-2) + 1024*a(n-3) for n>5.
Empirical g.f.: x*(11 - 392*x + 3072*x^2 - 8192*x^3 + 16384*x^4) / ((1 - 8*x)*(1 - 40*x + 128*x^2)). - Colin Barker, Oct 11 2018

A233259 Number of 4 X n 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).

Original entry on oeis.org

48, 2080, 221696, 23896064, 2647261184, 294517735424, 32835998056448, 3662495243829248, 408547159030366208, 45573786789742641152, 5083813692357704941568, 567106285442412421578752
Offset: 1

Views

Author

R. H. Hardin, Dec 06 2013

Keywords

Comments

Row 4 of A233256.

Examples

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

Links

Crossrefs

Cf. A233256.

Formula

Empirical: a(n) = 160*a(n-1) -6144*a(n-2) +86016*a(n-3) -393216*a(n-4) for n>8.

A233260 Number of 5Xn 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabeled 6-colorings with no clashing color pairs).

Original entry on oeis.org

236, 32896, 10620928, 3439984640, 1159192379392, 393427728465920, 134179300927602688, 45829217084770353152, 15662712220567239393280, 5353914504847465071509504, 1830206096861520940880625664
Offset: 1

Views

Author

R. H. Hardin, Dec 06 2013

Keywords

Comments

Row 5 of A233256

Examples

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

Links

Formula

Empirical: a(n) = 512*a(n-1) -65536*a(n-2) +2490368*a(n-3) +17825792*a(n-4) -2818572288*a(n-5) +51539607552*a(n-6) -274877906944*a(n-7) for n>11
Showing 1-10 of 12 results. Next

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

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