A233113 -id:A233113 - cp's OEIS frontend

A233106 Number of n X 1 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order.

1, 2, 6, 23, 99, 452, 2136, 10313, 50469, 249062, 1235466, 6147803, 30650439, 152986472, 764135196, 3818284493, 19084248009, 95399716682, 476934013326, 2384476356383, 11921800651179, 59607259863692, 298031069141856

Offset: 1

R. H. Hardin, Dec 04 2013

nonn

Column 1 of A233113.

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Empirical: a(n) = 9*a(n-1) - 23*a(n-2) + 15*a(n-3).
Conjectures from Colin Barker, Feb 19 2018: (Start)
G.f.: x*(1 - 7*x + 11*x^2) / ((1 - x)*(1 - 3*x)*(1 - 5*x)).
a(n) = (75 + 10*3^n + 3*5^n) / 120.
(End)

A233107 Number of n X 2 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order.

Original entry on oeis.org

2, 19, 313, 6046, 123352, 2565169, 53692063, 1126297996, 23643610702, 496455294319, 10425137467813, 218924920833946, 4597402575582052, 96545308753707469, 2027450466493247563, 42576452675015933896

Offset: 1

R. H. Hardin, Dec 04 2013

nonn

Column 2 of A233113.

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A233113.

Empirical: a(n) = 29*a(n-1) - 175*a(n-2) + 147*a(n-3).
Conjectures from Colin Barker, Mar 19 2018: (Start)
G.f.: x*(2 - 7*x)*(1 - 16*x) / ((1 - x)*(1 - 7*x)*(1 - 21*x)).
a(n) = (105 + 18*7^n + 5*21^n) / 168.
(End)

A233108 Number of n X 3 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order.

Original entry on oeis.org

6, 313, 24912, 2154065, 189286871, 16683923848, 1471365099497, 129774107522700, 11446271884607256, 1009582054691903383, 89047037607095248482, 7854117302435219663735, 692748031461206544348041

Offset: 1

R. H. Hardin, Dec 04 2013

nonn

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Column 3 of A233113.

Empirical: a(n) = 111*a(n-1) - 2128*a(n-2) + 10532*a(n-3) - 17559*a(n-4) + 9045*a(n-5).

Empirical g.f.: x*(6 - 353*x + 2937*x^2 - 8295*x^3 + 7230*x^4) / ((1 - x)*(1 - 18*x + 27*x^2)*(1 - 92*x + 335*x^2)). - Colin Barker, Oct 07 2018

A233109 Number of nX4 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order.

Original entry on oeis.org

23, 6046, 2154065, 794723482, 294285758398, 109015274761891, 40385221182281560, 14960955484170769147, 5542380989283805407733, 2053210330075493118514936, 760624844506193044187974495

Offset: 1

R. H. Hardin, Dec 04 2013

nonn

Column 4 of A233113

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Empirical: a(n) = 445*a(n-1) -29415*a(n-2) +684239*a(n-3) -6544703*a(n-4) +26009211*a(n-5) -37153497*a(n-6) +17033721*a(n-7)

A233110 Number of nX5 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order.

Original entry on oeis.org

99, 123352, 189286871, 294285758398, 457873555330159, 712427482567592092, 1108502928092713640626, 1724777533707727108574193, 2683671364004795423834363994, 4175664311828036646078204783047

Offset: 1

R. H. Hardin, Dec 04 2013

nonn

Column 5 of A233113

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Empirical: a(n) = 1903*a(n-1) -587832*a(n-2) +77760886*a(n-3) -5287016185*a(n-4) +188909127665*a(n-5) -3121291574501*a(n-6) +5961157912045*a(n-7) +488488284983722*a(n-8) -6216213294870140*a(n-9) +30096051456844829*a(n-10) -50425593642643659*a(n-11) -57028414169574032*a(n-12) +289749791197635300*a(n-13) -320983517286000000*a(n-14) +114316383888000000*a(n-15)

A233111 Number of nX6 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order.

Original entry on oeis.org

452, 2565169, 16683923848, 109015274761891, 712427482567592092, 4655818309443587944819, 30426461543542804692390703, 198841429156093687790582460286, 1299458167307093973096933933936847

Offset: 1

R. H. Hardin, Dec 04 2013

nonn

Column 6 of A233113

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

R. H. Hardin, Table of n, a(n) for n = 1..210

A233112 Number of nX7 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order.

Original entry on oeis.org

2136, 53692063, 1471365099497, 40385221182281560, 1108502928092713640626, 30426461543542804692390703, 835153023014356911992288011287, 22923486223269810222694953768125080

Offset: 1

R. H. Hardin, Dec 04 2013

nonn

Column 7 of A233113

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

R. H. Hardin, Table of n, a(n) for n = 1..210

A233105 Number of n X n 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order.

Original entry on oeis.org

1, 19, 24912, 794723482, 457873555330159, 4655818309443587944819, 835153023014356911992288011287, 2642740111638617064845250032401005032917, 147523503812676026261878057522783598121057848912309

Offset: 1

R. H. Hardin, Dec 04 2013

nonn

Diagonal of A233113

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

cp's OEIS Frontend

A233106 Number of n X 1 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order.

Views

Author

Keywords

Comments

Examples

Links

Formula

A233107 Number of n X 2 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A233108 Number of n X 3 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order.

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

A233109 Number of nX4 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order.

Views

Author

Keywords

Comments

Examples

Links

Formula

A233110 Number of nX5 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order.

Views

Author

Keywords

Comments

Examples

Links

Formula

A233111 Number of nX6 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order.

Views

Author

Keywords

Comments

Examples

Links

A233112 Number of nX7 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order.

Views

Author

Keywords

Comments

Examples

Links

A233105 Number of n X n 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order.

Views

Author

Keywords

Comments

Examples