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Table of Non-Overlapping Rook Paths
From: Heiner Marxen
Subject: Re: Self-Avoiding Walks of a Rook on a Chessboard
To: sfinch@.com (Steven Finch)
Date: Mon, 9 Sep 96 20:47:01 +0200
Cc: nl3242t@nlccmail.snads.philips.nl
...
----- snip -----
This is a table of results regarding a puzzle from the rec.games.puzzle FAQ:
> ==> competition/games/chess/rook.paths.p <==
> How many non-overlapping paths can a rook take from one corner to the opposite
> on an MxN chess board?
Computed Jul-9-1994 by heiner@drb.insel.de (Heiner Marxen) on an Apollo
HP9000-710. Computation stopped, when the number length exceeded 63 decimal
places. In brackets is given floor(log10(W)) (i.e. length-1). Up to W(8,8)
the results have been confirmed by andreas@hit.ordina.nl (Andreas Gammel).
W(1, N) is not given, it is proven to be 1.
W(2, N) is not given, it is proven to be 2^(N-1).
W(M, N) is given below for M=3..12 up to some appropriate N.
Timing: W( 3,*) < 1 sec
W( 4,*) < 1 sec
W( 5,*) < 1 sec
W( 6,*) < 1 sec
W( 7,*) < 1 sec
W( 8,*) < 3 sec
W( 9,*) < 11 sec
W(10,*) < 51 sec, using 0.7 MB
W(11,*) < 4.5 min, using 3.2 MB
W(12,*) < 28 min, using 14.7 MB
While it is relatively cheap to compute larger N, current methods do not
extend beyond M=12. M=13 is expected to take 7.5 times the time and space
as M=12.
W(3, 1) = 1 [ 0]
W(3, 2) = 4 [ 0]
W(3, 3) = 12 [ 1]
W(3, 4) = 38 [ 1]
W(3, 5) = 125 [ 2]
W(3, 6) = 414 [ 2]
W(3, 7) = 1369 [ 3]
W(3, 8) = 4522 [ 3]
W(3, 9) = 14934 [ 4]
W(3,10) = 49322 [ 4]
W(3,11) = 162899 [ 5]
W(3,12) = 538020 [ 5]
W(3,13) = 1776961 [ 6]
W(3,14) = 5868904 [ 6]
W(3,15) = 19383672 [ 7]
W(3,16) = 64019918 [ 7]
W(3,17) = 211443425 [ 8]
W(3,18) = 698350194 [ 8]
W(3,19) = 2306494009 [ 9]
W(3,20) = 7617832222 [ 9]
W(3,21) = 25159990674 [10]
W(3,22) = 83097804242 [10]
W(3,23) = 274453403399 [11]
W(3,24) = 906458014440 [11]
W(3,25) = 2993827446721 [12]
W(3,26) = 9887940354604 [12]
W(3,27) = 32657648510532 [13]
W(3,28) = 107860885886198 [14]
W(3,29) = 356240306169125 [14]
W(3,30) = 1176581804393574 [15]
W(3,31) = 3885985719349849 [15]
W(3,32) = 12834538962443122 [16]
W(3,33) = 42389602606679214 [16]
W(3,34) = 140003346782480762 [17]
W(3,35) = 462399642954121499 [17]
W(3,36) = 1527202275644845260 [18]
W(3,37) = 5044006469888657281 [18]
W(3,38) = 16659221685310817104 [19]
W(3,39) = 55021671525821108592 [19]
W(3,40) = 181724236262774142878 [20]
W(3,41) = 600194380314143537225 [20]
W(3,42) = 1982307377205204754554 [21]
W(3,43) = 6547116511929757800889 [21]
W(3,44) = 21623656912994478157222 [22]
W(3,45) = 71418087250913192272554 [22]
W(3,46) = 235877918665734054974882 [23]
W(3,47) = 779051843248115357197199 [23]
W(3,48) = 2573033448410080126566480 [24]
W(3,49) = 8498152188478355736896641 [24]
W(3,50) = 28067490013845147337256404 [25]
W(3,51) = 92700622230013797748665852 [25]
W(3,52) = 306169356703886540583253958 [26]
W(3,53) = 1011208692341673419498427725 [27]
W(3,54) = 3339795433728906799078537134 [27]
W(3,55) = 11030594993528393816734039129 [28]
W(3,56) = 36431580414314088249280654522 [28]
W(3,57) = 120325336236470658564576002694 [29]
W(3,58) = 397407589123726063943008662602 [29]
W(3,59) = 1312548103607648850393601990499 [30]
W(3,60) = 4335051899946672615123814634100 [30]
W(3,61) = 14317703803447666695765045892801 [31]
W(3,62) = 47288163310289672702418952312504 [31]
W(3,63) = 156182193734316684803021902830312 [32]
W(3,64) = 515834744513239727111484660803438 [32]
W(3,65) = 1703686427274035866137475885240625 [33]
W(3,66) = 5626894026335347325523912316525314 [33]
W(3,67) = 18584368506280077842709212834816569 [34]
W(3,68) = 61379999545175580853651550820975022 [34]
W(3,69) = 202724367141806820403663865297741634 [35]
W(3,70) = 669553100970596042064643146714199922 [35]
W(3,71) = 2211383670053594946597593305440341399 [36]
W(3,72) = 7303704111131380881857423063035224120 [36]
W(3,73) = 24122496003447737592169862494546013761 [37]
W(3,74) = 79671192121474593658367010546673265404 [37]
W(3,75) = 263136072367871518567270894134565809972 [38]
W(3,76) = 869079409225089149360179692950370695318 [38]
W(3,77) = 2870374300043138966647809972985677895925 [39]
W(3,78) = 9480202309354506049303609611907404383094 [39]
W(3,79) = 31310981228106657114558638808707891045209 [40]
W(3,80) = 103413145993674477392979526038031077518722 [41]
W(3,81) = 341550419209130089293497216922801123601374 [41]
W(3,82) = 1128064403621064745273471176806434448322842 [42]
W(3,83) = 3725743630072324325113910747342104468569899 [42]
W(3,84) = 12305295293838037720615203418832747854032540 [43]
W(3,85) = 40641629511586437486959521003840348030667521 [43]
W(3,86) = 134230183828597350181493766430353791946035104 [44]
W(3,87) = 443332180997378488031440820294901723868772832 [44]
W(3,88) = 1464226726820732814275816227315058963552353598 [45]
W(3,89) = 4836012361459576930858889502240078614525833625 [45]
W(3,90) = 15972263811199463606852484734035294807129854474 [46]
W(3,91) = 52752803795057967751416343704345963035915397049 [46]
W(3,92) = 174230675196373366861101515847073183914876045622 [47]
W(3,93) = 575444829384178068334720891245565514780543533914 [47]
W(3,94) = 1900565163348907571865264189583769728256506647362 [48]
W(3,95) = 6277140319430900783930513459996874699550063475999 [48]
W(3,96) = 20731986121641609923656804569574393826906697075360 [49]
W(3,97) = 68473098684355730554900927168720056180270154702081 [49]
W(3,98) = 226151282174708801588359586075734562367717161181604 [50]
W(3,99) = 746926945208482135319979685395923743283421638246892 [50]
W(4, 1) = 1 [ 0]
W(4, 2) = 8 [ 0]
W(4, 3) = 38 [ 1]
W(4, 4) = 184 [ 2]
W(4, 5) = 976 [ 2]
W(4, 6) = 5382 [ 3]
W(4, 7) = 29739 [ 4]
W(4, 8) = 163496 [ 5]
W(4, 9) = 896476 [ 5]
W(4,10) = 4913258 [ 6]
W(4,11) = 26932712 [ 7]
W(4,12) = 147657866 [ 8]
W(4,13) = 809563548 [ 8]
W(4,14) = 4438573234 [ 9]
W(4,15) = 24335048679 [10]
W(4,16) = 133419610132 [11]
W(4,17) = 731487691902 [11]
W(4,18) = 4010463268476 [12]
W(4,19) = 21987818897998 [13]
W(4,20) = 120550710615560 [14]
W(4,21) = 660932932108467 [14]
W(4,22) = 3623639655071710 [15]
W(4,23) = 19867014742102743 [16]
W(4,24) = 108923158053332350 [17]
W(4,25) = 597183548805361659 [17]
W(4,26) = 3274126433946876296 [18]
W(4,27) = 17950768950492095067 [19]
W(4,28) = 98417123591603463702 [19]
W(4,29) = 539583025251001060895 [20]
W(4,30) = 2958325040532073565578 [21]
W(4,31) = 16219352047588503102931 [22]
W(4,32) = 88924434346993487396018 [22]
W(4,33) = 487538281475956033249386 [23]
W(4,34) = 2672983839031408908893916 [24]
W(4,35) = 14654936597168716548095928 [25]
W(4,36) = 80347349479245087653282074 [25]
W(4,37) = 440513442384128454230014613 [26]
W(4,38) = 2415164833424179619327303842 [27]
W(4,39) = 13241414702442720218413491702 [28]
W(4,40) = 72597555618379554849853118946 [28]
W(4,41) = 398024319923418028799874399486 [29]
W(4,42) = 2182213407890434581197668112870 [30]
W(4,43) = 11964232131576855889677682759218 [31]
W(4,44) = 65595257540202524866505250371022 [31]
W(4,45) = 359633427740791094233174799503049 [32]
W(4,46) = 1971730993956723856944164669063190 [33]
W(4,47) = 10810238461291424483325071391724948 [34]
W(4,48) = 59268356559875272059272626241138728 [34]
W(4,49) = 324945476631869566441981252258628354 [35]
W(4,50) = 1781550373795873303046713142646399904 [36]
W(4,51) = 9767551674424287869585654837546753491 [36]
W(4,52) = 53551708172737889118984976149020490376 [37]
W(4,53) = 293603304472623945552890943383774309553 [38]
W(4,54) = 1609713365616383912308859851071670622980 [39]
W(4,55) = 8825435817550996535425583680276951174743 [39]
W(4,56) = 48386451298357329879562930164488161283378 [40]
W(4,57) = 265284198723909326010530260334192363603579 [41]
W(4,58) = 1454450661377099111998484352537278610029664 [42]
W(4,59) = 7974190458972193232276413494739024904035175 [42]
W(4,60) = 43719402221425103400219631051992513835552796 [43]
W(4,61) = 239696573643804342555403482756570411438692093 [44]
W(4,62) = 1314163609227566871627401045217315241219245708 [45]
W(4,63) = 7205050808879866983229734138168052327879819646 [45]
W(4,64) = 39502506989257958949229300006423441433947940968 [46]
W(4,65) = 216576967994895917886491309999855977545519956240 [47]
W(4,66) = 1187407753098236361825775237145885246834124153838 [48]
W(4,67) = 6510097473296561785818236153147375605099451792511 [48]
W(4,68) = 35692346627549762778296694042467212171999382378068 [49]
W(4,69) = 195687332333607524724325619649009538171416821980512 [50]
W(4,70) = 1072877959957001642510955492475520008145421812677274 [51]
W(4,71) = 5882174912575126770545069198885225692099460671417212 [51]
W(4,72) = 32249690079862283655389057301327920860488527689575482 [52]
W(4,73) = 176812577950330447532667716843020938774666605024948768 [53]
W(4,74) = 969394981595903209253602872718018527127931582396345810 [53]
W(4,75) = 5314817764872508909440911901788699733363068719878363267 [54]
W(4,76) = 29139090267726828672101491129568926164985894708877166896 [55]
W(4,77) = 159758362223187186115178951141088305982105151431979627194 [56]
W(4,78) = 875893312582340209091675503057602610992285820401216578964 [56]
W(4,79) = 4802184275992258467685155546646227537411153018593911630510 [57]
W(4,80) = 26328519112217101072702784576501163145680120126686374204632 [58]
W(4,81) = 144349087582472991120586287593712757432209074233139096049251 [59]
W(4,82) = 791410219355015665893496929969521863582820793544444873396002 [59]
W(4,83) = 4338996150160658424307562918695547774468533439918803080849363 [60]
W(4,84) = 23789037759017784414170843912582277633825901413761601754767642 [61]
W(4,85) = 130426093482249307737692978033716384106914364975908009829969139 [62]
W(4,86) = 715075827503448965720246577184436431183396047561961739178927508 [62]
W(5, 1) = 1 [ 0]
W(5, 2) = 16 [ 1]
W(5, 3) = 125 [ 2]
W(5, 4) = 976 [ 2]
W(5, 5) = 8512 [ 3]
W(5, 6) = 79384 [ 4]
W(5, 7) = 752061 [ 5]
W(5, 8) = 7110272 [ 6]
W(5, 9) = 67005561 [ 7]
W(5,10) = 630588698 [ 8]
W(5,11) = 5933085772 [ 9]
W(5,12) = 55827318685 [10]
W(5,13) = 525343024814 [11]
W(5,14) = 4943673540576 [12]
W(5,15) = 46521924780255 [13]
W(5,16) = 437788749723725 [14]
W(5,17) = 4119750109152730 [15]
W(5,18) = 38768318191017931 [16]
W(5,19) = 364823700357765771 [17]
W(5,20) = 3433121323699285343 [18]
W(5,21) = 32306898830469680384 [19]
W(5,22) = 304019468350280601960 [20]
W(5,23) = 2860931888452842047170 [21]
W(5,24) = 26922391858409506569346 [22]
W(5,25) = 253349332040459400463497 [23]
W(5,26) = 2384107785665647075602841 [24]
W(5,27) = 22435306570786253414376286 [25]
W(5,28) = 211124255357254403803629035 [26]
W(5,29) = 1986754718952099249909705783 [27]
W(5,30) = 18696072161887025777926174219 [28]
W(5,31) = 175936722811233879876002194230 [29]
W(5,32) = 1655627458297809088928561146142 [30]
W(5,33) = 15580046262485573366602344892679 [31]
W(5,34) = 146613805131471376745432664782147 [32]
W(5,35) = 1379688320110304714211546245580297 [33]
W(5,36) = 12983360325051785394010690753755824 [34]
W(5,37) = 122178062155844407644383553938446977 [35]
W(5,38) = 1149739243033589421875218557417568767 [36]
W(5,39) = 10819457303924976036891705581751397328 [37]
W(5,40) = 101814961140745872340842375048060231946 [38]
W(5,41) = 958115182757920062930691301192563148820 [38]
W(5,42) = 9016206391929460524310669044081210076821 [39]
W(5,43) = 84845725404196114901576363520487874379017 [40]
W(5,44) = 798428608046062434880163743522733414588407 [41]
W(5,45) = 7513498636607157729408193670863232681920390 [42]
W(5,46) = 70704708214864950083606947513647345537262118 [43]
W(5,47) = 665356580939853752053276134819021418639396968 [44]
W(5,48) = 6261243288843657065357857850224698884802176769 [45]
W(5,49) = 58920537716352105174088000259119255665492079697 [46]
W(5,50) = 554463323757096922520674423477990122778083506296 [47]
W(5,51) = 5217698094877483315102286426467829236802676569144 [48]
W(5,52) = 49100404378080664911893537773290991329131770825243 [49]
W(5,53) = 462052358387296083996390535982583964471803842259664 [50]
W(5,54) = 4348077874213379753210582213331364334190995696757907 [51]
W(5,55) = 40916967216033474439392434831868055709765577197806606 [52]
W(5,56) = 385043289147814764671944162318304565362251761032381066 [53]
W(5,57) = 3623395002249142164514054390586296632495523620963741656 [54]
W(5,58) = 34097442319749028372310159050866684931685088503458994545 [55]
W(5,59) = 320869121922101159215665175346923664922094331427493512823 [56]
W(5,60) = 3019493146658339323244254859288829893628462954690802111431 [57]
W(5,61) = 28414509966247661726751143332414281043429575467454819233066 [58]
W(5,62) = 267390696851064779318845260078933906991615238282107051472837 [59]
W(5,63) = 2516242048426211709667710768894843343869700246318618288763345 [60]
W(5,64) = 23678737221716939195460736230952396136448836826924249211488495 [61]
W(5,65) = 222825382306047707107147110468051060454712279103671557540920124 [62]
W(6, 1) = 1 [ 0]
W(6, 2) = 32 [ 1]
W(6, 3) = 414 [ 2]
W(6, 4) = 5382 [ 3]
W(6, 5) = 79384 [ 4]
W(6, 6) = 1262816 [ 6]
W(6, 7) = 20562673 [ 7]
W(6, 8) = 336067810 [ 8]
W(6, 9) = 5493330332 [ 9]
W(6,10) = 89803472792 [10]
W(6,11) = 1468381290905 [12]
W(6,12) = 24012936982592 [13]
W(6,13) = 392716580997352 [14]
W(6,14) = 6422777815120738 [15]
W(6,15) = 105043595925333255 [17]
W(6,16) = 1717976646746942760 [18]
W(6,17) = 28097347987645295129 [19]
W(6,18) = 459529700981496318610 [20]
W(6,19) = 7515570007661530339293 [21]
W(6,20) = 122916531487036730334780 [23]
W(6,21) = 2010289859051351461718841 [24]
W(6,22) = 32878127252299185360551934 [25]
W(6,23) = 537719101299048122399217869 [26]
W(6,24) = 8794352250919537166665750722 [27]
W(6,25) = 143830917261013287829855929053 [29]
W(6,26) = 2352342978307852368872254574110 [30]
W(6,27) = 38472378495706095194731534070125 [31]
W(6,28) = 629212627935457125950913558054726 [32]
W(6,29) = 10290721464101586255448326254366900 [34]
W(6,30) = 168303914369885958800758915526318474 [35]
W(6,31) = 2752596860300114955964065429361536989 [36]
W(6,32) = 45018498254837163421818726088041699166 [37]
W(6,33) = 736273885345044284085688553892457204990 [38]
W(6,34) = 12041699640279371326340375422350041719446 [40]
W(6,35) = 196941020336151050199143987475335247318191 [41]
W(6,36) = 3220954404252653214796052011262240269847376 [42]
W(6,37) = 52678447875240888447093955411712504021593807 [43]
W(6,38) = 861551739720563513304275975426292082337631174 [44]
W(6,39) = 14090608781288751611582325118090142798190478571 [46]
W(6,40) = 230450763051941815978795941071686604125891198442 [47]
W(6,41) = 3769003526784804976816338101329440702079133017666 [48]
W(6,42) = 61641746795668086369885223391335280193549793452454 [49]
W(6,43) = 1008145766120479656207584228935637479155797947389803 [51]
W(6,44) = 16488142185777157345793212901099082094584264689337958 [52]
W(6,45) = 269662227303264323330785234671779693565559562284410182 [53]
W(6,46) = 4410303842290033896172439105038616399715156984924650402 [54]
W(6,47) = 72130161409086529608951854829851816002712963801157839787 [55]
W(6,48) = 1179682935903881340573479585181430128337758733576064749582 [57]
W(6,49) = 19293618675966098340238272567572020098236154654850930308513 [58]
W(6,50) = 315545567613362204775242670274937424600545170340425654393866 [59]
W(6,51) = 5160722149260222882522006042304141173305206572051170726255899 [60]
W(6,52) = 84403191917113277982043589954202883741227100622483260510931370 [61]
W(7, 1) = 1 [ 0]
W(7, 2) = 64 [ 1]
W(7, 3) = 1369 [ 3]
W(7, 4) = 29739 [ 4]
W(7, 5) = 752061 [ 5]
W(7, 6) = 20562673 [ 7]
W(7, 7) = 575780564 [ 8]
W(7, 8) = 16230458696 [10]
W(7, 9) = 459133264944 [11]
W(7,10) = 13021391001373 [13]
W(7,11) = 369886375079581 [14]
W(7,12) = 10516022622412960 [16]
W(7,13) = 299104709252534435 [17]
W(7,14) = 8509249843020438582 [18]
W(7,15) = 242108399244641421526 [20]
W(7,16) = 6888987223916209602814 [21]
W(7,17) = 196026708756588099010848 [23]
W(7,18) = 5578053961718932115597017 [24]
W(7,19) = 158728232358841952835386863 [26]
W(7,20) = 4516767757061854076293758285 [27]
W(7,21) = 128529392946828650026263986056 [29]
W(7,22) = 3657444470628097260059276129911 [30]
W(7,23) = 104076657765409856754477709745139 [32]
W(7,24) = 2961618386677007033270145520935213 [33]
W(7,25) = 84276199971056311916655735952493374 [34]
W(7,26) = 2398174816704752797880344822184042261 [36]
W(7,27) = 68242787100453955377302714478054648107 [37]
W(7,28) = 1941926041419538974702064193716647084705 [39]
W(7,29) = 55259712700067457288109534327783675144232 [40]
W(7,30) = 1572477945946381248285033609383989297686043 [42]
W(7,31) = 44746647790998627587080956886160310005281831 [43]
W(7,32) = 1273316740806483427313381046105817307586846279 [45]
W(7,33) = 36233675692409546441709234287707870915534849271 [46]
W(7,34) = 1031070442214508266274915132931315543866586325969 [48]
W(7,35) = 29340281846986110522947656665859832241205885310805 [49]
W(7,36) = 834911082471996636214835976970788344507895569395788 [50]
W(7,37) = 23758344222309014069307120706577255213069748966360167 [52]
W(7,38) = 676070700298502294742505635302397334395963883959746576 [53]
W(7,39) = 19238360532925369429324082506655154157817860293909785086 [55]
W(7,40) = 547449424796172337585875033769696541620043771522378195680 [56]
W(7,41) = 15578295884357565376851837864957286643179170407188712931097 [58]
W(7,42) = 443298123387175906645334539013271126629214319094846266510703 [59]
W(7,43) = 12614552172957266162754921884082628317178368107658852162942435 [61]
W(7,44) = 358961426023118212075880447781043309190930699711987637234825422 [62]
W(8, 1) = 1 [ 0]
W(8, 2) = 128 [ 2]
W(8, 3) = 4522 [ 3]
W(8, 4) = 163496 [ 5]
W(8, 5) = 7110272 [ 6]
W(8, 6) = 336067810 [ 8]
W(8, 7) = 16230458696 [10]
W(8, 8) = 789360053252 [11]
W(8, 9) = 38603590450777 [13]
W(8,10) = 1896597558069886 [15]
W(8,11) = 93467039444263314 [16]
W(8,12) = 4614618337661429084 [18]
W(8,13) = 228073604373821861695 [20]
W(8,14) = 11279473113082310507710 [22]
W(8,15) = 558044223844519272676141 [23]
W(8,16) = 27615252735468871470811414 [25]
W(8,17) = 1366753277825934668137076421 [27]
W(8,18) = 67649988491247877009826179754 [28]
W(8,19) = 3348630780028864342606939528796 [30]
W(8,20) = 165760096281759281320462505161838 [32]
W(8,21) = 8205416825208627070745138116189675 [33]
W(8,22) = 406187052394187392981104614349928914 [35]
W(8,23) = 20107328500402658550260618474407661259 [37]
W(8,24) = 995369653976679229916147394744461631862 [38]
W(8,25) = 49273731974940819821278920458508202878484 [40]
W(8,26) = 2439198484184433596893476728623799086885414 [42]
W(8,27) = 120747792943791055034522895801327511963432478 [44]
W(8,28) = 5977388544335051496416595326191182018457058058 [45]
W(8,29) = 295899279840505530094389836812405244881667389490 [47]
W(8,30) = 14647935233496589129036456010199652559263277836688 [49]
W(8,31) = 725118462492647692988084722278893003659985608641076 [50]
W(8,32) = 35895627062566388083935009671515920695904074372155822 [52]
W(8,33) = 1776945646150852533075668101575409311770674152575813774 [54]
W(8,34) = 87964361270723890578982618813196559425922915921058696490 [55]
W(8,35) = 4354510778019048249754424714679316431911711590512399671822 [57]
W(8,36) = 215561893595098859119198477042428878229923922076695648446616 [59]
W(8,37) = 10670987531642199733767344184779455758812607825620208530754289 [61]
W(8,38) = 528247239655076022639138626026596710475391145777374640581299248 [62]
W(9, 1) = 1 [ 0]
W(9, 2) = 256 [ 2]
W(9, 3) = 14934 [ 4]
W(9, 4) = 896476 [ 5]
W(9, 5) = 67005561 [ 7]
W(9, 6) = 5493330332 [ 9]
W(9, 7) = 459133264944 [11]
W(9, 8) = 38603590450777 [13]
W(9, 9) = 3266598486981642 [15]
W(9,10) = 278065795198022522 [17]
W(9,11) = 23771282378421890188 [19]
W(9,12) = 2037735840792349459408 [21]
W(9,13) = 174984693167026909838637 [23]
W(9,14) = 15043327348304711749778561 [25]
W(9,15) = 1294228007560478044464188014 [27]
W(9,16) = 111401146002669479384505121978 [29]
W(9,17) = 9591952169949534737730355918193 [30]
W(9,18) = 826065710868247080536084489862479 [32]
W(9,19) = 71150993564506741272339856061929630 [34]
W(9,20) = 6128943783062333876582603620198505730 [36]
W(9,21) = 527977306544125135454395294504563125572 [38]
W(9,22) = 45484259345514485351068027777025301545897 [40]
W(9,23) = 3918479546539241769759398250012944054510834 [42]
W(9,24) = 337583285634430860804615268053379664145921966 [44]
W(9,25) = 29083641153528380527459094396248923993016340645 [46]
W(9,26) = 2505645019079261238922247609702313958466238144018 [48]
W(9,27) = 215869961362426587102675423311604136568954170008975 [50]
W(9,28) = 18597994903505429719479007252265636491707991905764589 [52]
W(9,29) = 1602288968361241067618077777520322003452542320827440669 [54]
W(9,30) = 138043539684264894073780318033790199928833447987641095721 [56]
W(9,31) = 11893006976190049707367325260692275966419374243112121329050 [58]
W(9,32) = 1024630981725134896354010679789518697887157202045987313308025 [60]
W(9,33) = 88276161108401674474605358278807467284382800622036425378560849 [61]
W(10, 1) = 1 [ 0]
W(10, 2) = 512 [ 2]
W(10, 3) = 49322 [ 4]
W(10, 4) = 4913258 [ 6]
W(10, 5) = 630588698 [ 8]
W(10, 6) = 89803472792 [10]
W(10, 7) = 13021391001373 [13]
W(10, 8) = 1896597558069886 [15]
W(10, 9) = 278065795198022522 [17]
W(10,10) = 41044208702632496804 [19]
W(10,11) = 6089404268345231341903 [21]
W(10,12) = 906580953466894744400498 [23]
W(10,13) = 135288601620380186876749340 [26]
W(10,14) = 20221960762421426978177915020 [28]
W(10,15) = 3026065681121995657331049388171 [30]
W(10,16) = 453185482144046050100591881851156 [32]
W(10,17) = 67906377136138785860332269950994237 [34]
W(10,18) = 10179082557233479970303228344175800420 [37]
W(10,19) = 1526228176156908710986332283696378704075 [39]
W(10,20) = 228880101898341785124844342319833252034368 [41]
W(10,21) = 34328133980704869751128957847492962027086339 [43]
W(10,22) = 5149075772858876772566186868242636225227785322 [45]
W(10,23) = 772384965220063796353652440454914953517385724185 [47]
W(10,24) = 115865960644277193428781102926511290847321363256944 [50]
W(10,25) = 17381609739197519526053951623488735699982848662415477 [52]
W(10,26) = 2607548759432666745290988842316475496639723282284945054 [54]
W(10,27) = 391183572947515020996899765778041431530387519057393739900 [56]
W(10,28) = 58685758842883064736798327346461808492522248662328214646778 [58]
W(10,29) = 8804152510176938170406818598810538332506462124299587477196407 [60]
W(11, 1) = 1 [ 0]
W(11, 2) = 1024 [ 3]
W(11, 3) = 162899 [ 5]
W(11, 4) = 26932712 [ 7]
W(11, 5) = 5933085772 [ 9]
W(11, 6) = 1468381290905 [12]
W(11, 7) = 369886375079581 [14]
W(11, 8) = 93467039444263314 [16]
W(11, 9) = 23771282378421890188 [19]
W(11,10) = 6089404268345231341903 [21]
W(11,11) = 1568758030464750013214100 [24]
W(11,12) = 405769626908332575325415852 [26]
W(11,13) = 105254779101613880966774835935 [29]
W(11,14) = 27359159340297390348383198021785 [31]
W(11,15) = 7122279869660711072637404183374811 [33]
W(11,16) = 1856142093992389592553419995975884802 [36]
W(11,17) = 484113693792985461605880230438107747321 [38]
W(11,18) = 126337279423591171925726036967916419191362 [41]
W(11,19) = 32983315991883281531834136292768362227121240 [43]
W(11,20) = 8613620105239316668434905938544164592578613427 [45]
W(11,21) = 2249933301163550920289224253384142773479790084977 [48]
W(11,22) = 587787195612441867174772624756700112451411013427747 [50]
W(11,23) = 153574263854157949295238694815398240054569577197118620 [53]
W(11,24) = 40128336079541729364546167294577728230493220863041951121 [55]
W(11,25) = 10485969151009714664954623915756804637031982438632780525770 [58]
W(11,26) = 2740209439452757438166514486341433373341552521899494619474776 [60]
W(11,27) = 716096746061120221627388772630197996466023391473373548188553526 [62]
W(12, 1) = 1 [ 0]
W(12, 2) = 2048 [ 3]
W(12, 3) = 538020 [ 5]
W(12, 4) = 147657866 [ 8]
W(12, 5) = 55827318685 [10]
W(12, 6) = 24012936982592 [13]
W(12, 7) = 10516022622412960 [16]
W(12, 8) = 4614618337661429084 [18]
W(12, 9) = 2037735840792349459408 [21]
W(12,10) = 906580953466894744400498 [23]
W(12,11) = 405769626908332575325415852 [26]
W(12,12) = 182413291514248049241470885236 [29]
W(12,13) = 82268836815726830679889460105219 [31]
W(12,14) = 37193725396722922783032448209106010 [34]
W(12,15) = 16846202313728151287180674479245984129 [37]
W(12,16) = 7640727338151282172126324003660331010496 [39]
W(12,17) = 3469100388909590205715294900257993390563552 [42]
W(12,18) = 1576284772533300863581687076502683539033501838 [45]
W(12,19) = 716642916765212333854968453908978776402603450901 [47]
W(12,20) = 325954856930969667989728262086849968817540859838588 [50]
W(12,21) = 148303348279908186931630991269722589449346216313412255 [53]
W(12,22) = 67491295363568713863906352429499974689304367833264451136 [55]
W(12,23) = 30720012839495700528737852549579220081913228189938181470886 [58]
W(12,24) = 13984666944967076917330642396948362451680659502211894069905088 [61]
----- snip -----
Later I could add:
----- snip -----
## Computed on an SGI IRIX workstation (R4400, 45 MHz)
## @ 20.May.1995
NUM_WORDS = 8
sizeof(Number ) = 32
sizeof(Umap ) = 256
sizeof(DUUdef ) = 52
sizeof(DIUUdef ) = 92
TIME(13,13) real 1:07:39.69 user 1:06:44.30 sys 6.15
TIME(13,20) real 1:43:49.92 user 1:42:31.51 sys 9.23
Memory: 4.45 MB
W(13, 1) = 1
W(13, 2) = 4096
W(13, 3) = 1776961
W(13, 4) = 809563548
W(13, 5) = 525343024814
W(13, 6) = 392716580997352
W(13, 7) = 299104709252534435
W(13, 8) = 228073604373821861695
W(13, 9) = 174984693167026909838637
W(13,10) = 135288601620380186876749340
W(13,11) = 105254779101613880966774835935
W(13,12) = 82268836815726830679889460105219
W(13,13) = 64528039343270018963357185158482118
W(13,14) = 50750325376483472808082060840001661852
W(13,15) = 39998656352715392458211293438906385119970
W(13,16) = 31576310786416112227691519471158189108721865
W(13,17) = 24958818638415495836841739030575979692614256862
W(13,18) = 19747257240041545726918596816733037839421460249574
W(13,19) = 15635505553916576127200056066433174366794262435841915
W(13,20) = 12386943669551230803145944623665136996719815206609431897
----- snip -----
From: Heiner Marxen
Subject: W(14,20) and W(15,20)
To: sfinch@.com (Steven Finch)
Date: Fri, 13 Sep 96 2:29:33 +0200
Cc: nl3242t@nlccmail.snads.philips.nl
...I currently have access to a faster and larger machine...
----- snip -----
## Computed on HP9000/819
## Tue Sep 10 1996
NUM_WORDS = 8
sizeof(Number ) = 32
sizeof(Umap ) = 256
sizeof(DUUdef ) = 52
sizeof(DIUUdef ) = 92
TIME(14,20) real 3:32:42.8 user 3:31:55.9 sys 13.2
Memory: 12.088 MB (196938 slots)
W(14, 1) = 1
W(14, 2) = 8192
W(14, 3) = 5868904
W(14, 4) = 4438573234
W(14, 5) = 4943673540576
W(14, 6) = 6422777815120738
W(14, 7) = 8509249843020438582
W(14, 8) = 11279473113082310507710
W(14, 9) = 15043327348304711749778561
W(14,10) = 20221960762421426978177915020
W(14,11) = 27359159340297390348383198021785
W(14,12) = 37193725396722922783032448209106010
W(14,13) = 50750325376483472808082060840001661852
W(14,14) = 69450664761521361664274701548907358996488
W(14,15) = 95262966612892063156874389817827456761021038
W(14,16) = 130909894803647282919756617695448131233103278776
W(14,17) = 180157634504083966622313860098254618575340454467000
W(14,18) = 248216244130010747317113802567503531005799632575522258
W(14,19) = 342293437654879699827408687514517113078005631286155981913
W(14,20) = 472360617372958252809412594672907599431812810074227874196332
## Computed on HP9000/819
## Wed Sep 11 1996
NUM_WORDS = 8
sizeof(Number ) = 32
sizeof(Umap ) = 256
sizeof(DUUdef ) = 52
sizeof(DIUUdef ) = 92
TIME(15,20) real 16:34:22.6 user 16:29:16.5 sys 1:07.6
Memory: 33.357 MB (542895 slots)
W(15, 1) = 1
W(15, 2) = 16384
W(15, 3) = 19383672
W(15, 4) = 24335048679
W(15, 5) = 46521924780255
W(15, 6) = 105043595925333255
W(15, 7) = 242108399244641421526
W(15, 8) = 558044223844519272676141
W(15, 9) = 1294228007560478044464188014
W(15,10) = 3026065681121995657331049388171
W(15,11) = 7122279869660711072637404183374811
W(15,12) = 16846202313728151287180674479245984129
W(15,13) = 39998656352715392458211293438906385119970
W(15,14) = 95262966612892063156874389817827456761021038
W(15,15) = 227449714676812739631826459327989863387613323440
W(15,16) = 544153218633291055333005955373503380344455231720156
W(15,17) = 1303949463726800479567050586474874803419007600650103638
W(15,18) = 3128711042823236250260024108446485968800356758589577016646
W(15,19) = 7514901779717963705978192506823563289469102955658338970126326
W(15,20) = 18065251836996975790472937289751595742358854920978934398187863788
----- snip -----
Please, let me be informed of additional results.
Best regards,
--
Heiner Marxen heiner@drb.insel.de
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