A189355 -id:A189355 - cp's OEIS frontend

A189186 T(n,k) = Number of n X k array permutations with each element making a single king move.

0, 1, 1, 0, 9, 0, 1, 33, 33, 1, 0, 185, 192, 185, 0, 1, 913, 4081, 4081, 913, 1, 0, 4777, 47936, 251720, 47936, 4777, 0, 1, 24577, 733465, 10599449, 10599449, 733465, 24577, 1, 0, 127385, 9925824, 524539713, 1339732352, 524539713, 9925824, 127385, 0, 1

Offset: 1

R. H. Hardin, Apr 18 2011

Table starts
.0.......1...........0................1.....................0
.1.......9..........33..............185...................913
.0......33.........192.............4081.................47936
.1.....185........4081...........251720..............10599449
.0.....913.......47936.........10599449............1339732352
.1....4777......733465........524539713..........212852911361
.0...24577.....9925824......24377674329........30863909708032
.1..127385...142150545....1162453545201......4646631858824169
.0..658801..1982789568...54868164490816....689003645197185280
.1.3410313.27997733409.2600517767888745.102804050401764094481

			Some solutions for 5X3
..3..2..1....3..5..4....1..3..4....1..0..5....4..0..1....3..2..1....3..0..5
..0..5..8....0..1..2....0..8..2....7..3..2....6..5..2....0..8..7....6..1..2
..9..6..4...10..6..7...10..6..5....4..9.11....9..3..7....4..9..5....7..8..4
.13.14..7...13..8.14....7.11.14....6.14..8...10..8.14....6.14.13...10.12.13
.10.12.11....9.12.11....9.12.13...10.12.13...13.12.11...10.12.11....9.14.11

R. H. Hardin, Table of n, a(n) for n = 1..144

Cf. A189355.

A189348 Number of n X 2 array permutations with each element moving one space diagonally, horizontally or vertically.

Original entry on oeis.org

1, 4, 13, 45, 160, 565, 2005, 7108, 25209, 89401, 317056, 1124425, 3987721, 14142276, 50154949, 177872293, 630816160, 2237161405, 7933993245, 28137553540, 99788579953, 353895752689, 1255075518976, 4451069407761, 15785519335825

Offset: 1

R. H. Hardin, Apr 20 2011

nonn

Column 2 of A189355.

			Some solutions for 3 X 2:
..1..3....2..0....3..0....1..0....1..0....3..0....1..0....1..3....1..3....1..0
..0..5....3..1....5..1....4..5....3..5....4..1....4..2....5..0....0..2....3..2
..2..4....5..4....2..4....2..3....2..4....5..2....5..3....2..4....5..4....5..4

R. H. Hardin, Table of n, a(n) for n = 1..200

Cf. A189355.

Empirical: a(n) = 3*a(n-1) +3*a(n-2) -3*a(n-3) -3*a(n-4) +a(n-5).

Empirical g.f.: x*(1 + x - 2*x^2 - 3*x^3 + x^4) / ((1 - x)*(1 - 2*x - 5*x^2 - 2*x^3 + x^4)). - Colin Barker, May 02 2018

A189349 Number of nX3 array permutations with each element moving one space diagonally, horizontally or vertically.

Original entry on oeis.org

0, 13, 48, 557, 3632, 30769, 229248, 1815601, 13960720, 108880333, 843387440, 6554347309, 50856496800, 394905287105, 3065356528128, 23798261444545, 184745059744352, 1434227515809901, 11134091807034928, 86436190372455949

Offset: 1

R. H. Hardin Apr 20 2011

nonn

Column 3 of A189355

			Some solutions for 4X3
..3..0..1....3..4..1....3..2..5....3..0..1....3..2..5....1..4..5....4..2..1
..7..5..2....0..8..2....0..7..1....4..8..2....7..0..1....0..8..2....0..5..8
.10..4.11....9.11..5....9..6..4....9.11..5....9.10..4...10..3.11....9..3.11
..6..9..8...10..6..7...10.11..8...10..6..7....6.11..8....6..9..7....6..7.10

R. H. Hardin, Table of n, a(n) for n = 1..200

Empirical: a(n) = 2*a(n-1) +41*a(n-2) +44*a(n-3) -118*a(n-4) +118*a(n-6) -44*a(n-7) -41*a(n-8) -2*a(n-9) +a(n-10)

A189350 Number of nX4 array permutations with each element moving one space diagonally, horizontally or vertically.

Original entry on oeis.org

1, 45, 557, 12592, 237297, 4791913, 94635005, 1883785285, 37399042560, 743166198493, 14763119513829, 293302192368977, 5826899299462793, 115761639593312944, 2299800733947890517, 45689485687194056453

Offset: 1

R. H. Hardin Apr 20 2011

nonn

Column 4 of A189355

			Some solutions for 3X4
..4..0..3..7....4..5..3..7....4..2..3..7....5..6..1..2....4..2..3..7
..8..1..5..2....0..6..1..2....5..0..1.11....0..9.10..3....0.10..1.11
..9.10.11..6....9..8.11.10....9..8..6.10....4..8.11..7....9..8..5..6

R. H. Hardin, Table of n, a(n) for n = 1..200

Empirical: a(n) = 8*a(n-1) +268*a(n-2) +100*a(n-3) -14506*a(n-4) -22855*a(n-5) +347444*a(n-6) +727264*a(n-7) -4361775*a(n-8) -10839894*a(n-9) +28941588*a(n-10) +87051904*a(n-11) -86750184*a(n-12) -379741329*a(n-13) +15880784*a(n-14) +854458520*a(n-15) +430764327*a(n-16) -969033120*a(n-17) -802207572*a(n-18) +802207572*a(n-19) +969033120*a(n-20) -430764327*a(n-21) -854458520*a(n-22) -15880784*a(n-23) +379741329*a(n-24) +86750184*a(n-25) -87051904*a(n-26) -28941588*a(n-27) +10839894*a(n-28) +4361775*a(n-29) -727264*a(n-30) -347444*a(n-31) +22855*a(n-32) +14506*a(n-33) -100*a(n-34) -268*a(n-35) -8*a(n-36) +a(n-37)

A189351 Number of nX5 array permutations with each element moving one space diagonally, horizontally or vertically.

Original entry on oeis.org

0, 160, 3632, 237297, 10252800, 519621497, 24728774144, 1206541811872, 58289324009008, 2827118724742121, 136905250232923136, 6633862748392813081, 321370023775584504336, 15569943269307141603680, 754313155570494656470048

Offset: 1

R. H. Hardin Apr 20 2011

nonn

Column 5 of A189355

			Some solutions for 3X5
..6..2..7..4..3....1..0..7..2..3....5..6..3..2..9....5..2..8..4..3
..0.11..1.14..8....6.11.12.14..4....0..1.13.14..4...10..0..1.13.14
..5.10.13.12..9....5.10.13..8..9...11.10..7.12..8...11..6..7.12..9

R. H. Hardin, Table of n, a(n) for n = 1..200

A189352 Number of nX6 array permutations with each element moving one space diagonally, horizontally or vertically.

Original entry on oeis.org

1, 565, 30769, 4791913, 519621497, 64731638400, 7675175968337, 927311536349401, 111267210412798665, 13385995390731369181, 1608827786945127170673, 193432938477399402591673, 23253629565778621415892480

Offset: 1

R. H. Hardin Apr 20 2011

nonn

Column 6 of A189355

			Some solutions for 3X6
..7..0..1.10..3..4....6..0..3..2..5.11....7..0..8..2..5.11....6..0..3..2..5.11
.12.14..2.15.11..5...12..8..1.15.16..4...12..1.15..3..4.17...12..1.14.15.16..4
.13..6..8..9.17.16...13.14..7..9.17.10....6.14.13.16..9.10...13..7..8..9.17.10

R. H. Hardin, Table of n, a(n) for n = 1..200

A189353 Number of nX7 array permutations with each element moving one space diagonally, horizontally or vertically.

Original entry on oeis.org

0, 2005, 229248, 94635005, 24728774144, 7675175968337, 2239546267804672, 669245368116765065, 198265824869143635104, 58936758437348449273685, 17497862834694963378124992, 5197536868658118835508778253

Offset: 1

R. H. Hardin Apr 20 2011

nonn

Column 7 of A189355

			Some solutions for 3X7
..1..2..3..4.11..6.13....1..2..3.10..5..4.13....1..0.10..2.11.12..5
..0..7.16..9.10.20..5...14..0..8.17.18.11..6...14..7.17.18..3..4..6
.15.14..8.18.17.12.19...15..7..9.16.19.20.12...15.16..8..9.19.20.13

R. H. Hardin, Table of n, a(n) for n = 1..90

A189354 Number of nX8 array permutations with each element moving one space diagonally, horizontally or vertically.

Original entry on oeis.org

1, 7108, 1815601, 1883785285, 1206541811872, 927311536349401, 669245368116765065, 494966160398383884544, 362995012557977063017785, 267122042433316923724049137, 196343414435260084855304091712

Offset: 1

R. H. Hardin Apr 20 2011

nonn

Column 8 of A189355

			Some solutions for 3X8
..1..0..3..2.12.13..7..6....1..0..3..2..5.13.15..6....1..0..3.11..5..4..7.15
.16.17.11.19..4.22..5.14...16.10.18.20.21..4.23..7...16.18..2.19.20.12..6.23
..8..9.10.18.21.20.23.15...17..8..9.11.19.12.14.22...17..8..9.10.21.22.13.14

R. H. Hardin, Table of n, a(n) for n = 1..20

A189347 Number of n X n array permutations with each element moving one space diagonally, horizontally or vertically.

Original entry on oeis.org

0, 4, 48, 12592, 10252800, 64731638400, 2239546267804672, 494966160398383884544, 658664151315274081588459520, 5410532537689878793764236394523648, 271891121107496085701096037929377481809920

Offset: 1

R. H. Hardin, Apr 20 2011

			Some solutions for 3 X 3:
..1..2..5....4..0..1....1..2..5....4..2..1....3..2..1....3..0..5....1..0..5
..0..8..4....6..3..2....7..0..8....0..5..8....4..0..8....6..1..2....6..8..2
..3..6..7....7..8..5....3..6..4....3..6..7....7..6..5....7..8..4....3..4..7

Diagonal of A189355.

a(9)-a(11) from Pontus von Brömssen, Aug 28 2024

cp's OEIS Frontend

A189186 T(n,k) = Number of n X k array permutations with each element making a single king move.

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A189348 Number of n X 2 array permutations with each element moving one space diagonally, horizontally or vertically.

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A189349 Number of nX3 array permutations with each element moving one space diagonally, horizontally or vertically.

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A189350 Number of nX4 array permutations with each element moving one space diagonally, horizontally or vertically.

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A189351 Number of nX5 array permutations with each element moving one space diagonally, horizontally or vertically.

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A189352 Number of nX6 array permutations with each element moving one space diagonally, horizontally or vertically.

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A189353 Number of nX7 array permutations with each element moving one space diagonally, horizontally or vertically.

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A189354 Number of nX8 array permutations with each element moving one space diagonally, horizontally or vertically.

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A189347 Number of n X n array permutations with each element moving one space diagonally, horizontally or vertically.

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