A189186 -id:A189186 - cp's OEIS frontend

A189355 T(n,k) is the number of n X k array permutations with each element moving one space diagonally, horizontally or vertically.

0, 1, 1, 0, 4, 0, 1, 13, 13, 1, 0, 45, 48, 45, 0, 1, 160, 557, 557, 160, 1, 0, 565, 3632, 12592, 3632, 565, 0, 1, 2005, 30769, 237297, 237297, 30769, 2005, 1, 0, 7108, 229248, 4791913, 10252800, 4791913, 229248, 7108, 0, 1, 25209, 1815601, 94635005

Offset: 1

R. H. Hardin, Apr 20 2011

Table starts
.0.....1.........0............1................0....................1
.1.....4........13...........45..............160..................565
.0....13........48..........557.............3632................30769
.1....45.......557........12592...........237297..............4791913
.0...160......3632.......237297.........10252800............519621497
.1...565.....30769......4791913........519621497..........64731638400
.0..2005....229248.....94635005......24728774144........7675175968337
.1..7108...1815601...1883785285....1206541811872......927311536349401
.0.25209..13960720..37399042560...58289324009008...111267210412798665
.1.89401.108880333.743166198493.2827118724742121.13385995390731369181

			Some solutions for 5X3
..1..0..5....4..5..1....4..0..5....4..5..1....3..5..1....1..2..5....3..2..5
..6..3..2....7..0..2....6..1..2....0..8..2....0..8..2....0..7..8....0..1..4
..7..8..4....3..6.11....3..8..7....3..6..7....9..4..7...10..3..4....9..8..7
.12.11.10...10.14..8...12.11.14...13.14.10...12..6.14...13..6.14...12..6.10
..9.14.13....9.12.13...13..9.10....9.12.11...13.10.11....9.12.11...13.14.11

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

Cf. A189186.

A189179 Number of n X 2 array permutations with each element making a single king move.

Original entry on oeis.org

1, 9, 33, 185, 913, 4777, 24577, 127385, 658801, 3410313, 17648609, 91343481, 472746833, 2446730345, 12663143361, 65538688857, 339198332209, 1755536122697, 9085854920609, 47024245778489, 243376070611729, 1259603657442857

Offset: 1

R. H. Hardin, Apr 18 2011

nonn

Column 2 of A189186.

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

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

Cf. A189186.

Empirical: a(n) = 5*a(n-1) + 4*a(n-2) - 16*a(n-3).

Empirical g.f.: x*(1 + 4*x - 16*x^2) / (1 - 5*x - 4*x^2 + 16*x^3). - Colin Barker, Mar 01 2018

A189180 Number of nX3 array permutations with each element making a single king move.

Original entry on oeis.org

0, 33, 192, 4081, 47936, 733465, 9925824, 142150545, 1982789568, 27997733409, 393091648000, 5533702536417, 77804055183232, 1094555504869945, 15394211168981632, 216536449010819041, 3045646510935265408

Offset: 1

R. H. Hardin Apr 18 2011

nonn

Column 3 of A189186

			Some solutions for 4X3
..3..0..5....4..2..1....3..5..1....3..2..5....1..3..5....3..2..5....3..2..5
..1..6..2....0..3..8....6..0..2....4..0..1....0..6..2....0..1..8....4..0..1
..9..4.11....9..5.11...10..4.11....7..9.11....9.11..4....9..6..4....9.10..7
.10..7..8...10..6..7....7..9..8....6..8.10....7..8.10...10.11..7....6.11..8

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

Empirical: a(n) = 8*a(n-1) +94*a(n-2) -88*a(n-3) -488*a(n-4) +152*a(n-5) -638*a(n-6) -72*a(n-7) +9*a(n-8)

A189181 Number of nX4 array permutations with each element making a single king move.

Original entry on oeis.org

1, 185, 4081, 251720, 10599449, 524539713, 24377674329, 1162453545201, 54868164490816, 2600517767888745, 123049732810644217, 5826272557390770993, 275793998574143720745, 13056461887253840005544, 618083925262185774246993

Offset: 1

R. H. Hardin Apr 18 2011

nonn

Column 4 of A189186

			Some solutions for 3X4
..1..2..3..6....5..0..3..2....5..0..1..2....4..0..3..2....1..6..3..2
..0..8..7.11....8..1..9..6....8.10..3.11....1..8..9.11....8..0.10.11
..9..4..5.10....4.10.11..7....9..4..6..7....5..6..7.10....9..4..5..7

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

Empirical: a(n) = 50*a(n-1) +189*a(n-2) -17418*a(n-3) +111208*a(n-4) +452547*a(n-5) -4449430*a(n-6) +190937*a(n-7) +29532742*a(n-8) -4370254*a(n-9) +186074662*a(n-10) -567421032*a(n-11) -487743654*a(n-12) -150818946*a(n-13) -265001610*a(n-14) +6374532886*a(n-15) -3311165152*a(n-16) -3325788742*a(n-17) +2609479826*a(n-18) -1073359914*a(n-19) +294380347*a(n-20) +4801462*a(n-21) -20168455*a(n-22) +4712116*a(n-23) -541926*a(n-24) -30393*a(n-25) +13302*a(n-26) -675*a(n-27)

A189182 Number of nX5 array permutations with each element making a single king move.

Original entry on oeis.org

0, 913, 47936, 10599449, 1339732352, 212852911361, 30863909708032, 4646631858824169, 689003645197185280, 102804050401764094481, 15300259132449601539840, 2279486758722355781575289

Offset: 1

R. H. Hardin Apr 18 2011

nonn

Column 5 of A189186

			Some solutions for 3X5
..5..0..7..2..3....1..2..6..7..8....1..0..7..2..3....5..0..7..2..9
..1.10..6.14..4....0.12.11..3..4...11.10..6..4..8...11..1.12..4..3
.11.12.13..8..9....5.10.13.14..9....5.12.13.14..9....6.10..8.14.13

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

Empirical: a(n) = 114*a(n-1) +9317*a(n-2) -508866*a(n-3) -20910348*a(n-4) +704525664*a(n-5) +19358697488*a(n-6) -428304917728*a(n-7) -8879601094240*a(n-8) +129853332142720*a(n-9) +2190323609648896*a(n-10) -20574172318548480*a(n-11) -314606162399573504*a(n-12) +1598037911119250432*a(n-13) +27684023072295867392*a(n-14) -32346791780760006656*a(n-15) -1499684717324405215232*a(n-16) -3695155586595907993600*a(n-17) +46583697668722445025280*a(n-18) +290219562521732580573184*a(n-19) -593905480603069347004416*a(n-20) -8401632685478568054226944*a(n-21) -6539590799133706090971136*a(n-22) +96348126155652764263251968*a(n-23) +264417463146912245959622656*a(n-24) +12682495240626001051385856*a(n-25) -1744238428870058772105527296*a(n-26) -5693069153240876119306010624*a(n-27) -4564434382539862336212041728*a(n-28) -7943580772549846384227909632*a(n-29) -31586327988680906132309409792*a(n-30) +143766153982154846382418034688*a(n-31) +511623793291640778265865486336*a(n-32) +551178593322357659823759163392*a(n-33) +202854802351241365026179645440*a(n-34) -2905957648388000419056778739712*a(n-35) -3155337356481894282288074588160*a(n-36) -1042822458306188258889227567104*a(n-37) -2453052645713081078335951339520*a(n-38) +6778721456546169282766280065024*a(n-39) -1504306134813089239960437915648*a(n-40) -10352521978401584357617218617344*a(n-41) -3016565382617002414243131162624*a(n-42) +6150339155711867029113958039552*a(n-43) +10412506380362096054859393400832*a(n-44) +6806793406325595977933081542656*a(n-45) +2721724352275152477557442478080*a(n-46) +569526346586061594312736505856*a(n-47) -1477517748051341183691492687872*a(n-48) -1912761063129875165619605733376*a(n-49) -508156074249026659194220052480*a(n-50) +54066805553079381002532421632*a(n-51) +19155126199747274898514378752*a(n-52) +8773476904398267578136395776*a(n-53)
Contribution from Vaclav Kotesovec, Sep 01 2012: (Start)
Empirical: G.f.: -(1 - 114*x - 8404*x^2 + 452720*x^3 + 17538672*x^4 - 555155552*x^5 - 14506192288*x^6 + 297522132352*x^7 + 5810955247360*x^8 - 77927468499968*x^9 - 1230827400698880*x^10 + 10139196103077888*x^11 + 149566628136468480*x^12 - 557358281707810816*x^13 - 10843389941491863552*x^14 - 5310040642240905216*x^15 + 455986646377081831424*x^16 + 2047404517133439008768*x^17 - 9189873733410207891456*x^18 - 88268012596050635259904*x^19 - 6448621366095173910528*x^20 + 1378703975728569971113984*x^21 + 3088276968654707456212992*x^22 - 2470628711959669566865408*x^23 - 28767883420911499955142656*x^24 - 86514759183212419861184512*x^25 - 72211531466119535757623296*x^26 - 51267266293593481651683328*x^27 - 218962196765555625742565376*x^28 + 2451936235318107505927651328*x^29 + 7612818543369496887342137344*x^30 + 6898474527655796275847102464*x^31 + 1761382792028209537112604672*x^32 - 44763611093749388131983949824*x^33 - 48501822621203236978549587968*x^34 - 13094996240823567727225470976*x^35 - 40738215697505864447443337216*x^36 + 97748004267381040026423918592*x^37 - 23263335095947805743468511232*x^38 - 155382127530337186609388060672*x^39 - 39259801019630566464401965056*x^40 + 98652847390601076741272240128*x^41 + 161478541720281995669430861824*x^42 + 104198714253491857781627551744*x^43 + 40398299441776989086276386816*x^44 + 7350369579983929771701567488*x^45 - 23233990515836094630374408192*x^46 - 29533799958373725631238111232*x^47 - 7832192715239216204734267392*x^48 + 864382638942304568740937728*x^49 + 299415301166388498688638976*x^50 + 135059681410071853111705600*x^51)/( - 1 + 114*x + 9317*x^2 - 508866*x^3 - 20910348*x^4 + 704525664*x^5 + 19358697488*x^6 - 428304917728*x^7 - 8879601094240*x^8 + 129853332142720*x^9 + 2190323609648896*x^10 - 20574172318548480*x^11 - 314606162399573504*x^12 + 1598037911119250432*x^13 + 27684023072295867392*x^14 - 32346791780760006656*x^15 - 1499684717324405215232*x^16 - 3695155586595907993600*x^17 + 46583697668722445025280*x^18 + 290219562521732580573184*x^19 - 593905480603069347004416*x^20 - 8401632685478568054226944*x^21 - 6539590799133706090971136*x^22 + 96348126155652764263251968*x^23 + 264417463146912245959622656*x^24 + 12682495240626001051385856*x^25 - 1744238428870058772105527296*x^26 - 5693069153240876119306010624*x^27 - 4564434382539862336212041728*x^28 - 7943580772549846384227909632*x^29 - 31586327988680906132309409792*x^30 + 143766153982154846382418034688*x^31 + 511623793291640778265865486336*x^32 + 551178593322357659823759163392*x^33 + 202854802351241365026179645440*x^34 - 2905957648388000419056778739712*x^35 - 3155337356481894282288074588160*x^36 - 1042822458306188258889227567104*x^37 - 2453052645713081078335951339520*x^38 + 6778721456546169282766280065024*x^39 - 1504306134813089239960437915648*x^40 - 10352521978401584357617218617344*x^41 - 3016565382617002414243131162624*x^42 + 6150339155711867029113958039552*x^43 + 10412506380362096054859393400832*x^44 + 6806793406325595977933081542656*x^45 + 2721724352275152477557442478080*x^46 + 569526346586061594312736505856*x^47 - 1477517748051341183691492687872*x^48 - 1912761063129875165619605733376*x^49 - 508156074249026659194220052480*x^50 + 54066805553079381002532421632*x^51 + 19155126199747274898514378752*x^52 + 8773476904398267578136395776*x^53)
Asymptotic: 0.019129360759172571821 * 148.938932254396291243461581^n
(End)

A189183 Number of nX6 array permutations with each element making a single king move.

Original entry on oeis.org

1, 4777, 733465, 524539713, 212852911361, 108943637068673, 51019657551661825, 24772194881412281568, 11859612477133400173321, 5710233425140480749753825, 2743236264948075503280904473, 1319063462694864224288387507313

Offset: 1

R. H. Hardin Apr 18 2011

nonn

Column 6 of A189186

			Some solutions for 3X6
..1..0..3..2..5.10....1..0..8..9..3..4....1..0..3..2..5..4....1..0..3..2..9.11
.12..6.15..4..9.17...12..6..2.10.17..5....7.12.15.14.11.16...13.12..7..4.16..5
.13..8..7.14.11.16...13.14..7.16.15.11...13..6..8..9.17.10....6.14.15..8.17.10

R. H. Hardin, Table of n, a(n) for n = 1..150

A189184 Number of nX7 array permutations with each element making a single king move.

Original entry on oeis.org

0, 24577, 9925824, 24377674329, 30863909708032, 51019657551661825, 76260881288534294528, 118756821701162151227761, 182058599536052537764772096, 280897765265782382194137678153

Offset: 1

R. H. Hardin Apr 18 2011

nonn

Column 7 of A189186

			Some solutions for 3X7
..1..0..3..2.10..6.12....1..0..3..2..5..4.13....1..0..3..2..5..6.13
.14..7.17..4..5.20.19...14.16..8.11.18.19..6...14..9..8.17.18..4.20
.15..9..8.16.11.18.13...15..7..9.10.17.20.12....7.16.15.10.11.12.19

R. H. Hardin, Table of n, a(n) for n = 1..46

A189185 Number of nX8 array permutations with each element making a single king move.

Original entry on oeis.org

1, 127385, 142150545, 1162453545201, 4646631858824169, 24772194881412281568, 118756821701162151227761, 594579828469677562655346609, 2929346624538378869533780899145, 14529411775016363663957822341921161

Offset: 1

R. H. Hardin Apr 18 2011

nonn

Column 8 of A189186

			Some solutions for 3X8
..1..0..3..2..5..4..7..6....1..0..3..2..5..4..7..6....1..0..3..2..5..4..7..6
.17.16..9.20.11.21.13.14...17.16..9.19.20.14.21.22...17.16.18.19.11.21.23.22
..8.10.19.18.12.22.23.15....8.18.10.12.11.13.23.15....8..9.10.20.12.13.14.15

R. H. Hardin, Table of n, a(n) for n = 1..15

A189178 Number of n X n array permutations with each element making a single king move.

Original entry on oeis.org

0, 9, 192, 251720, 1339732352, 108943637068673, 76260881288534294528, 594579828469677562655346609, 46342255378179654331792920815382272, 37825739518339601867409254032413815052514057

Offset: 1

R. H. Hardin, Apr 18 2011

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

Diagonal of A189186.

a(9)-a(10) from Pontus von Brömssen, Aug 28 2024

cp's OEIS Frontend

A189355 T(n,k) is the number of n X k array permutations with each element moving one space diagonally, horizontally or vertically.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A189179 Number of n X 2 array permutations with each element making a single king move.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A189180 Number of nX3 array permutations with each element making a single king move.

Views

Author

Keywords

Comments

Examples

Links

Formula

A189181 Number of nX4 array permutations with each element making a single king move.

Views

Author

Keywords

Comments

Examples

Links

Formula

A189182 Number of nX5 array permutations with each element making a single king move.

Views

Author

Keywords

Comments

Examples

Links

Formula

A189183 Number of nX6 array permutations with each element making a single king move.

Views

Author

Keywords

Comments

Examples

Links

A189184 Number of nX7 array permutations with each element making a single king move.

Views

Author

Keywords

Comments

Examples

Links

A189185 Number of nX8 array permutations with each element making a single king move.

Views

Author

Keywords

Comments

Examples

Links

A189178 Number of n X n array permutations with each element making a single king move.

Views

Author

Keywords

Examples

Crossrefs

Extensions