From: Doron Zeilberger zeilberg (AT) math.rutgers.edu
Date: Mon, 19 Aug 2013 09:10:35 -0400 (EDT)
To: njasloane@gmail.com
Subject: Hardin matrices

                  Rigorously derived generating functions for

                 enumerating k by n Hardin matrices for k from 1

                                    to , 11



                              By Shalosh B. Ekhad



               Definition: A Hardin matrix has entries from {0,1}

               with no adjacent 1's horizontally, vertically, or

             in the NW-SE direction, and whose top-left entry is 1



                 Definition:For a fixed k, Let f(k)(x) be the

                              generating function

                whose coefficient of x^n is the number of n by k

                We have the following (rigorously-derived) facts

              followed by the first, 20, terms of the enumerating

                      sequence (for  the sake of Sloane)

f[1](x) = -x/(x^2+x-1)

[1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584,

    4181, 6765]

f[2](x) = -x/(x^3+2*x^2+x-1)

[1, 1, 3, 6, 13, 28, 60, 129, 277, 595, 1278, 2745, 5896, 12664, 27201, 58425,

    125491, 269542, 578949, 1243524]

f[3](x) = -x*(x^3-x-2)/(x^5-4*x^3-5*x^2-x+1)

[2, 3, 13, 35, 112, 337, 1034, 3154, 9637, 29431, 89895, 274564, 838609,

    2561372, 7823242, 23894643, 72981777, 222909351, 680835436, 2079486057]

f[4](x) = x*(2*x^4-7*x^3-x^2+3*x+3)/(x^8-3*x^7+x^6+6*x^5-4*x^4-15*x^3-10*x^2-x+
1)

[3, 6, 35, 133, 587, 2448, 10414, 44024, 186414, 789100, 3340345, 14140347,

    59858152, 253389483, 1072638232, 4540650778, 19221306410, 81366888278,

    344439152622, 1458066449898]

f[5](x) = -x*(x^11-2*x^10-4*x^9+26*x^8-51*x^7+45*x^6-5*x^5-2*x^4-38*x^3-6*x^2+8
*x+5)/(x^13-2*x^12-8*x^11+37*x^10-57*x^9+13*x^8+68*x^7-38*x^6-69*x^5+14*x^4+48*
x^3+21*x^2+x-1)

[5, 13, 112, 587, 3631, 21166, 126119, 745178, 4416695, 26150120, 154877307,

    917205757, 5431915952, 32169045631, 190512481196, 1128258633821,

    6681806858103, 39571194265886, 234349700556332, 1387872742075595]

f[6](x) = x*(2*x^17+6*x^16-18*x^15-97*x^14+247*x^13-85*x^12-239*x^11-143*x^10+
1907*x^9-3792*x^8+3365*x^7-999*x^6-425*x^5+112*x^4+241*x^3+27*x^2-20*x-8)/(x^21
+3*x^20-6*x^19-29*x^18+32*x^17+154*x^16-148*x^15-1152*x^14+3926*x^13-5776*x^12+
3827*x^11+659*x^10-2727*x^9+732*x^8+1199*x^7-449*x^6-478*x^5+70*x^4+147*x^3+42*
x^2+x-1)

[8, 28, 337, 2448, 21166, 172082, 1428523, 11771298, 97268701, 802886174,

    6629901197, 54739811878, 451976078779, 3731849749697, 30812948919061,

    254414847888742, 2100639733295629, 17344457600010491, 143208852222784259,

    1182439709334842998]

f[7](x) = -x*(x^32+5*x^31-9*x^30-145*x^29-524*x^28-870*x^27+93*x^26+3283*x^25+
2794*x^24-13686*x^23-20581*x^22+52803*x^21+56597*x^20-219345*x^19+64005*x^18+
577213*x^17-1128820*x^16+695794*x^15+757117*x^14-2151205*x^13+2455581*x^12-\
1736815*x^11+824071*x^10-300738*x^9+133555*x^8-64864*x^7+9093*x^6+7249*x^5-601*
x^4-1336*x^3-131*x^2+47*x+13)/(x^34+5*x^33-14*x^32-173*x^31-545*x^30-561*x^29+
1405*x^28+5635*x^27+2585*x^26-23292*x^25-27097*x^24+92350*x^23+80904*x^22-\
365483*x^21+64683*x^20+942033*x^19-1353257*x^18-138325*x^17+2761082*x^16-\
4149918*x^15+3102284*x^14-897815*x^13-464722*x^12+477721*x^11-37244*x^10-112654
*x^9+27340*x^8+21164*x^7-5096*x^6-3711*x^5+192*x^4+432*x^3+85*x^2+x-1)

[13, 60, 1034, 10414, 126119, 1428523, 16566199, 190540884, 2197847780,

    25325358687, 291935092921, 3364727410265, 38782728207101, 447011297075966,

    5152298718205939, 59385855860517581, 684486816741728022,

    7889457806798773244, 90934612740867535991, 1048120674269761559923]

f[8](x) = x*(2*x^51-2*x^50-66*x^49+110*x^48+1629*x^47-4813*x^46-67688*x^45-\
234350*x^44-401990*x^43-658771*x^42-3161057*x^41-14624224*x^40-42871801*x^39-\
73761278*x^38-26604860*x^37+239859895*x^36+713783092*x^35+863260161*x^34-\
134128185*x^33-1800904161*x^32-1419374681*x^31+1935860639*x^30+2757350404*x^29-\
2352200353*x^28-3703928419*x^27+3855489166*x^26+3883942773*x^25-6335961004*x^24
-2037479016*x^23+8626282264*x^22-3109079348*x^21-7475315873*x^20+10724160854*x^
19-5285410006*x^18-736560408*x^17+1717885047*x^16+807074005*x^15-2824314771*x^
14+2737074476*x^13-1533773855*x^12+524079594*x^11-91693302*x^10+962499*x^9+
50560*x^8+1401445*x^7-213607*x^6-95198*x^5+4865*x^4+7163*x^3+545*x^2-108*x-21)/
(x^55-x^54-30*x^53+45*x^52+608*x^51-671*x^50-10138*x^49-2782*x^48+87637*x^47-\
234085*x^46-4214944*x^45-20510652*x^44-59224072*x^43-110007288*x^42-105839886*x
^41+67901250*x^40+405881894*x^39+511379314*x^38-211758176*x^37-1366907685*x^36-\
877760575*x^35+2023351213*x^34+2807416030*x^33-2482388885*x^32-5396581563*x^31+
3493944338*x^30+8290578844*x^29-6485990080*x^28-10036097232*x^27+12628340471*x^
26+6931675953*x^25-19704882159*x^24+5172378119*x^23+18258761486*x^22-\
21472294755*x^21+2246759550*x^20+18064627845*x^19-23143116063*x^18+15244941445*
x^17-5406913431*x^16+225285263*x^15+733571937*x^14-280040412*x^13-22625542*x^12
+40598266*x^11-4142351*x^10-3899000*x^9+677669*x^8+329977*x^7-47829*x^6-25328*x
^5+452*x^4+1243*x^3+170*x^2+x-1)

[21, 129, 3154, 44024, 745178, 11771298, 190540884, 3057290265, 49208639399,

    791176762937, 12725363193829, 204647839919537, 3291296999329711,

    52931964429099939, 851279732514835940, 13690693829364308175,

    220180543075683677274, 3541052375099195761698, 56948956408634393389871,

    915881298985498469592761]

f[9](x) = -x*(x^87-8*x^86-32*x^85+644*x^84-2907*x^83+2151*x^82+28450*x^81-\
120413*x^80+116834*x^79+1157261*x^78-6031619*x^77+528780*x^76+89023390*x^75-\
173350222*x^74-1151860848*x^73+2899238663*x^72+16085926699*x^71-24818469003*x^
70-214721214194*x^69-32166176169*x^68+2188056026979*x^67+4796619392584*x^66-\
9549922863025*x^65-69086644360435*x^64-122580631673293*x^63+159940777307292*x^
62+1443424730591592*x^61+3975212268405698*x^60+5403457632838150*x^59-\
2120616268353442*x^58-32309380383956217*x^57-97892798354412965*x^56-\
195561955588038608*x^55-292080690551658166*x^54-330897208018026283*x^53-\
271862382630883591*x^52-143153118189461025*x^51-46790597262700379*x^50-\
74824158811506368*x^49-191552329531247794*x^48-229734075077442510*x^47-\
70638447929915341*x^46+170575249373655168*x^45+235562083703165699*x^44+
52701963398566867*x^43-136611961721162593*x^42-101463611649363881*x^41+
49806571140121782*x^40+66964999027203092*x^39-31485119275002257*x^38-\
40080146559677170*x^37+34827698092835986*x^36+25676396868148593*x^35-\
36115472217148137*x^34-12698940642923466*x^33+31707377773650075*x^32-\
464132618617674*x^31-21925813281460471*x^30+9354081249342613*x^29+
9391601184461481*x^28-10350338655011577*x^27+436472375718377*x^26+
5310023826562667*x^25-3637822592998680*x^24-100789742203460*x^23+
1782281907825985*x^22-1375752912535871*x^21+444149479690459*x^20+90577465469715
*x^19-194792934082176*x^18+127237623941515*x^17-55330131274873*x^16+
18527504427376*x^15-5226077139205*x^14+1327892128274*x^13-295461449355*x^12+
46670718371*x^11-2100803693*x^10-763904766*x^9+31561542*x^8+42827155*x^7-\
3342239*x^6-1300016*x^5+19620*x^4+37360*x^3+2234*x^2-243*x-34)/(x^89-8*x^88-38*
x^87+695*x^86-2879*x^85-105*x^84+39914*x^83-136254*x^82+43847*x^81+1571198*x^80
-6700528*x^79-2570071*x^78+111939979*x^77-181278765*x^76-1496929050*x^75+
3457565706*x^74+20838665195*x^73-31494932814*x^72-278159240994*x^71-30990252773
*x^70+2847346843155*x^69+6019979527395*x^68-12381088034848*x^67-82879141747172*
x^66-127482845730036*x^65+246442107448472*x^64+1638150531308210*x^63+
3630394365861038*x^62+2148662678861166*x^61-12735538772455692*x^60-\
53901370391664446*x^59-124871036042872432*x^58-201657150023555253*x^57-\
226356673050150368*x^56-136563731814790740*x^55+67831170531569559*x^54+
272395901288262463*x^53+296803477374187509*x^52+64768558699537498*x^51-\
249495641012276252*x^50-324196672203238169*x^49-44674358779740500*x^48+
282871338108355230*x^47+247136946296363469*x^46-106868457992460011*x^45-\
280799538989855391*x^44-34278410467657420*x^43+226961599933750196*x^42+
95541176582994872*x^41-162855432975425412*x^40-99278700466055506*x^39+
117589053059603490*x^38+75307132119610574*x^37-89871633733075620*x^36-\
42509085580493654*x^35+69385711314076868*x^34+11682212847079777*x^33-\
48126804293022820*x^32+9585671646760248*x^31+24983151120411597*x^30-\
16816567234540602*x^29-5401968255267581*x^28+11825337408157360*x^27-\
4230674222649921*x^26-2982940342312306*x^25+3885196495123007*x^24-\
1464924827758540*x^23-440208193462827*x^22+852626156042858*x^21-524306069845407
*x^20+182611451591524*x^19-29496433268727*x^18-4478480115950*x^17+3500468879427
*x^16-538626934150*x^15-124488945147*x^14+55957856060*x^13-511179629*x^12-\
3049905478*x^11+272892045*x^10+130485447*x^9-15283855*x^8-5083216*x^7+417526*x^
6+171909*x^5+334*x^4-3520*x^3-341*x^2-x+1)

[34, 277, 9637, 186414, 4416695, 97268701, 2197847780, 49208639399,

    1105411581741, 24801939723742, 556713719650007, 12494370307905104,

    280426447918993931, 6293836975716291709, 141258681814255369288,

    3170396387349296944621, 71156151001790985434648, 1597023012652317575685103,

    35843461580050057669914634, 804467875227432424602919960]

f[10](x) = x*(2*x^140-8*x^139-166*x^138+530*x^137+10038*x^136-28642*x^135-\
512099*x^134-6845*x^133+67053158*x^132-671867789*x^131+3505238730*x^130-\
12918665069*x^129+51936488577*x^128-290508630419*x^127+1571862780978*x^126-\
6595301771377*x^125+21103600306469*x^124-53062135053784*x^123+104375899947829*x
^122-127819617568919*x^121-55383631860312*x^120+166407931582919*x^119+
5049487858662493*x^118-35851836130522311*x^117+103516424911961686*x^116-\
2977150632353102*x^115-1052667066155664532*x^114+3239580422553944906*x^113+
294587847712018263*x^112-25808743221387948854*x^111+48660876297316198051*x^110+
92689763761695831432*x^109-444622205366202713259*x^108-26797862361740843700*x^
107+2616280911930610765245*x^106-1937298339393183135326*x^105-\
12997405856990006989633*x^104+15722587930333675363488*x^103+
62609085363188732464212*x^102-83341107539460918630511*x^101-\
311768494169033347357592*x^100+319519647319106688859559*x^99+
1560238999075165024152454*x^98-622452933395972617548156*x^97-\
7161175350075342234119336*x^96-2647169772942112827812228*x^95+
27027779624096176266125939*x^94+35012462836686750294417288*x^93-\
69921369974591417277583146*x^92-205645166624731543488730589*x^91+
25966663649191012404998282*x^90+767658571140573448639801838*x^89+
838541959131582884728053761*x^88-1690028164835260464910958685*x^87-\
5399860590803306038139947060*x^86-1557191110726967439392965992*x^85+
19640394699608523201190588102*x^84+46916563919597007315030664223*x^83+
24021580551441864487681090494*x^82-144537522852998096942645414457*x^81-\
542185061141251679488656090757*x^80-1178670860512984229582727998747*x^79-\
1992417396805655572420337868132*x^78-2953677803279215843396245811225*x^77-\
4189715316965415828143835994294*x^76-5957402831496549082282848388125*x^75-\
8343337807559899022953746844400*x^74-10805046600478011461594406217677*x^73-\
11927196713099871015003606128668*x^72-9800583642061466966883467726012*x^71-\
3091114325122292780035155433332*x^70+7709052537594223363979137927392*x^69+
19751076088264736728041114171629*x^68+28713064287130768677560473368810*x^67+
30921960848150604198289102031504*x^66+25522373541084601609295105251194*x^65+
15170483550429893852984030907542*x^64+4570716155898167405163305861717*x^63-\
2268075682608984936188738264057*x^62-4139648209123703322368310381270*x^61-\
2670320092844874900332205350351*x^60-520907844355396519679810339666*x^59+
590548140031187954610620337831*x^58+551027297412087543161722583419*x^57+
120705467021083129608290324160*x^56-104701454739301104785311965428*x^55-\
73564531665536079768955087754*x^54+6079823064198573711834412629*x^53+
19933248156426030398405496800*x^52-454136038060919919356539247*x^51-\
6589801411534661488313849385*x^50+382393325552974530338644857*x^49+
2884723623219040312856507795*x^48-2057341430344632270414344*x^47-\
1210084991573563308168708830*x^46-76701064871627823887678250*x^45+
453608060153057943906721778*x^44+35592000363941526351469954*x^43-\
156569231723286739219032797*x^42-4610494752273247474202955*x^41+
50388130751016310762811305*x^40-4293946563270159799255087*x^39-\
14547440271961853747966549*x^38+3877587253186390546481027*x^37+
3345312888532805633967207*x^36-1890861373374053196682004*x^35-\
397596132586806008949183*x^34+617807706690723576116001*x^33-\
98271946990017304751155*x^32-118730846855512230482679*x^31+
67436016832386560570402*x^30+848786759719627104258*x^29-15141424289321106905249
*x^28+6288183106820427835265*x^27+209561996272466937685*x^26-\
1262356983194346790448*x^25+559516957091134544002*x^24-78228184981483286290*x^
23-29470828074758170416*x^22+14735772701453512492*x^21+966675479771951445*x^20-\
3488733657959634422*x^19+1856212832344850072*x^18-598803720718764665*x^17+
134012959989303766*x^16-21102471437243425*x^15+2268339616688237*x^14-\
174235502412321*x^13+17585725456002*x^12-2632415804625*x^11+97024371950*x^10+
39122234872*x^9-1437421859*x^8-1027677550*x^7+47458152*x^6+15453997*x^5-24417*x
^4-188806*x^3-8674*x^2+540*x+55)/(x^144-4*x^143-80*x^142+268*x^141+4626*x^140-\
16797*x^139-194370*x^138+942568*x^137+6173741*x^136-51966904*x^135+30823622*x^
134-173482730*x^133+19084417569*x^132-229388278225*x^131+1515048277124*x^130-\
6806121549780*x^129+22108890482902*x^128-49824816369981*x^127+48038583223469*x^
126+206220793190031*x^125-1344606621684746*x^124+3894283038558555*x^123-\
3610287259504860*x^122-20478528691642611*x^121+98896055697623523*x^120-\
133360240734211142*x^119-416152716286884582*x^118+2051928339652080981*x^117-\
1464060641862271975*x^116-11768953266039283828*x^115+30485855717824625944*x^114
+31881584987368210992*x^113-237287721700284945230*x^112+70479861283222322447*x^
111+1353495803669016970809*x^110-1477400305311275033910*x^109-\
6681284374793041534830*x^108+11334911392305227452211*x^107+
31654059020205093560956*x^106-65464241893517660895108*x^105-\
155064493302362591460511*x^104+316339473477803348079463*x^103+
803331621347308253138782*x^102-1263821778240196044265327*x^101-\
4231763919370660816517118*x^100+3545647785527365984648924*x^99+
21054479029887241145956386*x^98-18666482010666088718213*x^97-\
90275842318960556556559522*x^96-85010086560950163199752649*x^95+
284924931214625993098942944*x^94+671928809667505630371463788*x^93-\
306200417058198460712856000*x^92-3060190435437044888103700530*x^91-\
3211268355191497562112496191*x^90+6801719822107473884288311168*x^89+
23311860494947603387042632459*x^88+15109934142065527800602992758*x^87-\
58575994538411915176553755418*x^86-170343654568263198020439148213*x^85-\
139731406519188792279752062549*x^84+310053200148094815018820945755*x^83+
1221987183126716607796360869229*x^82+1890812502625088199534095746234*x^81+
572929408131589612029982687948*x^80-5056433364607766224423728932542*x^79-\
16531991141843803236365715142875*x^78-32890840255303313271510735281869*x^77-\
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41221015785297097947374200869637443594800397318*x^140-\
56622939440862974432165389584894221049195255080*x^139-\
106248864606453240717053283662271062145757449932*x^138+
111940865391957696283014739332048564379741219972*x^137+
277489528173805175499258476949801826442258118766*x^136-\
170034345172889820292311506888395232254114391894*x^135-\
700266400994846539055423364134366719684411693538*x^134+
80460469346612000242523755633911843867285945905*x^133+
1613689291622218630224872495308735970415082252100*x^132+
707996092849850748027169462134162177850766692636*x^131-\
3127456093766325417453570105534862013100977548300*x^130-\
3611441802623173144059780301616504420474611678133*x^129+
4169702495949758016079096604531149188971477606133*x^128+
10925566993014787795226642853989788614441605334022*x^127+
170445080699313991145773426473088659286765248045*x^126-\
22700055691447510738464165606737346784301404957031*x^125-\
21385071783513969672264656838210937211481684153488*x^124+
25508722630465802089770897681820817640043251718874*x^123+
69412696632447768287400557914958222833348980567222*x^122+
23798095955425122372917124798264219597498889194889*x^121-\
110066321662703026571573083441513737508507057787894*x^120-\
175297055722200928228517758711398639134796759853136*x^119-\
2194659845198082733364696827975088695421249744138*x^118+
329284156289537479114529624539882651815451448979046*x^117+
434882909022148630735748539536754317432667393705516*x^116-\
18282124138878547342665849005721409117035273359781*x^115-\
814178699796753584342842574303141422962649148104073*x^114-\
1136591070795475224156206660753841457706987033325968*x^113-\
247309595219527634034445857895546470915747607275455*x^112+
1590632567679781939694011035124063171029067071878252*x^111+
2894456898860676137169319273321361159412726338410109*x^110+
1952071579679066408370047862851515008055050027761778*x^109-\
1571310118219286826670953801884486185862170394715987*x^108-\
5763299741991191904507604646034113271462177096410361*x^107-\
7311697677200141797458515897308067872034782318185387*x^106-\
3738301311323349375915136321883510849362267046897619*x^105+
4500670994457640698212281503508385020695118324620329*x^104+
13632360768326988911950552388293146027271843096669496*x^103+
18344789278069658102711306108128188685911386421279573*x^102+
14685453030633188741404068853068565983299286481783198*x^101+
2307425655416796011511489377322283724686455164585147*x^100-\
15241390513470988819706267042756667439993944099194624*x^99-\
32240151519579518588336203197917188755619654651142961*x^98-\
43438005362899350854984219261313476654472060000049260*x^97-\
46170627454017295338119253722833971747855523319921669*x^96-\
41008265248704768040712109428627527408933498062003777*x^95-\
30908656853038909152001871080897874339955498139615918*x^94-\
19583123406573567272475473643367534101841930131780798*x^93-\
9987847457086274116336403352479708758209950270731029*x^92-\
3552580060731289561520678422923381890581003565555595*x^91-\
245470715115394119337931992445715477751511463113653*x^90+
834075007286650041997505495497899062260385653043698*x^89+
772582010243206944309880639208894342125001531904828*x^88+
386621094905901876996718122833850082722786385261622*x^87+
84854956147354598150286734329982796015118785601986*x^86-\
41401195165491281348939804217353903494348478933344*x^85-\
51089549110437712356805941785089090813678816412860*x^84-\
23318483318293546795071337055478510566398267100552*x^83-\
1887948563652466500794388232647954513152666678938*x^82+
4630221573748164278002321381757005607226970568085*x^81+
3108398310251572738706516682130075670076235954211*x^80+
582507312920161303947580183080798064054028269235*x^79-\
430097744593645544760870072909423219078238672686*x^78-\
343891522295702331055212191395063799064623917996*x^77-\
60242958166330769638705680896679043032375617954*x^76+
50892538870436566181754508426313527668541086644*x^75+
33982819024474518162714525887671662106548977842*x^74+
1904060035396864938577919438165066882834938306*x^73-\
6595584240190251016191576327345436337864005714*x^72-\
2591121903021520393728313158311512713515366647*x^71+
574039569389415512687241888499401773035889815*x^70+
695044950474166116837312984357075249653680118*x^69+
65800562335652117399874361019111742171756439*x^68-\
122964624660621888482742912782677914843405604*x^67-\
39688529434409524495771258632508297483580580*x^66+
16098195819563581540868520717789109627697328*x^65+
10414107384347089377685666214173746897790435*x^64-\
1434602146222440600306856044546533735529422*x^63-\
2131356626063294457951710308419601913489175*x^62+
20437204098065438020303260742402078259750*x^61+
387764900285467394447272256055451444352412*x^60+
25582829312880539639603315844476627557785*x^59-\
66757459067234942634960068141536874683286*x^58-\
6988012436212780545800711112094258371913*x^57+
11261039519888634064440231072015102870845*x^56+
1204765090071174058505184555286940330365*x^55-\
1883945703276506451056944715139438815104*x^54-\
136893977380238070950560413661752613180*x^53+
309200273552824945497769318774945513436*x^52+
1674270964320331143432776575934654854*x^51-\
48198815934912589729532272824126794047*x^50+
4375592102675388783732932739953974934*x^49+
6751217347320724528720546906311915653*x^48-\
1498362277854791024966526057890999778*x^47-766217755598746928991932398455610613
*x^46+331844832241296239594649178934919711*x^45+
50467601527151342942924834200434310*x^44-54500960601467067848257360970915506*x^
43+3978088432836095675943295893227156*x^42+6279202159034923978556679233948585*x
^41-1904855571383046154004467913062389*x^40-333273219769471482673361593612252*x
^39+313345040585157917116586680753299*x^38-41912629153039538319247076650856*x^
37-24557571950302622280548387383543*x^36+11580117298879884223590026345453*x^35-\
750063515237866727695545318593*x^34-973685215995082356702538414552*x^33+
379543299098662306890022821937*x^32-29237287465820286857375071768*x^31-\
24938892143548653251080065093*x^30+10986661583022770455370554954*x^29-\
1772407259294742414115364322*x^28-210597544432402642462068971*x^27+
199267716539874487776450358*x^26-58371655181682367221322608*x^25+
9933284284254729020920126*x^24-832401085688703747471575*x^23-\
49659712077576736111461*x^22+24107227497873732224787*x^21-\
2531360269690115673021*x^20-104329418366373715114*x^19+54554422131466534715*x^
18-3745351137564195223*x^17-510075830018997705*x^16+92127741020003912*x^15+
1274159669822044*x^14-1261184423385122*x^13+35160119703421*x^12+13344380578528*
x^11-636128064820*x^10-123970882060*x^9+5799151010*x^8+1042647728*x^7-25054744*
x^6-7079343*x^5-80092*x^4+27456*x^3+1365*x^2+x-1)
[89, 1278, 89895, 3340345, 154877307, 6629901197, 291935092921, 12725363193829,

    556713719650007, 24323608858322906, 1063228770141145384,

    46467826999734230731, 2030974556422845366545, 88766094139582331605246,

    3879654488735271050141403, 169565642639954148329642958,

    7411106619606782377852950977, 323912805472254569571065583672,

    14157065183943434981087679558140, 618754431478169665879994284792309]

               The first, 11, terms  of the enumerating sequence

                         for square Hardin matrices is

[1, 1, 13, 133, 3631, 172082, 16566199, 3057290265, 1105411581741,

    776531523355217, 1063228770141145384]

                   This took , 189.104, seconds, to generate