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A189182 Number of nX5 array permutations with each element making a single king move 1
0, 913, 47936, 10599449, 1339732352, 212852911361, 30863909708032, 4646631858824169, 689003645197185280, 102804050401764094481, 15300259132449601539840, 2279486758722355781575289 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Column 5 of A189186

LINKS

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

FORMULA

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)

EXAMPLE

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

CROSSREFS

Sequence in context: A224969 A263122 A286214 * A252427 A074887 A234993

Adjacent sequences: A189179 A189180 A189181 * A189183 A189184 A189185

KEYWORD

nonn

AUTHOR

R. H. Hardin Apr 18 2011

STATUS

approved

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Last modified December 4 14:04 EST 2022. Contains 358558 sequences. (Running on oeis4.)