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%I #12 Feb 19 2015 17:53:55
%S 1,16,178,1498,10980,85138,655090,5115398,39914386,312388874,
%T 2436283602,18994966598,148059349634,1154792660474,9007078544234,
%U 70254124462638,547921292697778,4273303250042966,33327954035543034,259932116476519958,2027268764564330754
%N Number of 2-colorings of a 4 X n rectangle such that no nontrivial subsquare has monochromatic corners.
%H Alois P. Heinz, <a href="/A255255/b255255.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: see Maple program.
%p gf:= -(4608*x^78 +3840*x^77 +84224*x^76 -320640*x^75 +246976*x^74 -756544*x^73 -2238400*x^72 +5321120*x^71 +12808672*x^70 +54862128*x^69 -56935120*x^68 -320396192*x^67 +196696056*x^66 +580449400*x^65 -800166640*x^64 +931676252*x^63 -3217094764*x^62 -2931282696*x^61 +15075340414*x^60 -25189807228*x^59 +8940907182*x^58 +72225838335*x^57 -79785446783*x^56 +16049408070*x^55 +94923048557*x^54 -184157650742*x^53 +84396466384*x^52 +63222211250*x^51 -205358037404*x^50
%p +102077559913*x^49 -54179691207*x^48 -58933050614*x^47 -72350094400*x^46 +119755954460*x^45 +391109674279*x^44 -31136120454*x^43 +7469466171*x^42 +4087734421*x^41 -259850982087*x^40 -250072129598*x^39 -106581496436*x^38 +208831935210*x^37 +402861489180*x^36 +109203162981*x^35 -275403863093*x^34 -334505242945*x^33 -114680900580*x^32 +196805363764*x^31 +294322652328*x^30 +163414286266*x^29
%p +9671161820*x^28 -93783726011*x^27 -117305441726*x^26 -63470276869*x^25 -4776176481*x^24 +17768047304*x^23 +14651146288*x^22 +7623498972*x^21 +4260618627*x^20 +1317986665*x^19 -720102442*x^18 -787824686*x^17 -195158015*x^16 +30687326*x^15 +15478943*x^14 +9512482*x^13 +14257207*x^12 +7365310*x^11 -194075*x^10 -1591059*x^9 -609139*x^8 -99289*x^7 +358*x^6 +4060*x^5 +1728*x^4 +632*x^3 +117*x^2 +14*x +1) /
%p (-2304*x^76 -4224*x^75 -48832*x^74 +106368*x^73 -28736*x^72 +387264*x^71 +1606752*x^70 -417728*x^69 -6732224*x^68 -32605960*x^67 -17678016*x^66 +104280356*x^65 +13666240*x^64 -287868964*x^63 +243731588*x^62 -345759930*x^61 +338343404*x^60 +2718472224*x^59 -4711903718*x^58 +5420902529*x^57 +8555023111*x^56 -23454331276*x^55 +9026831269*x^54
%p +16445485090*x^53 -42633850200*x^52 +27124456832*x^51 +15867136764*x^50 -59350410523*x^49 +30378083319*x^48 +11917445228*x^47 -36411691280*x^46 +24780724314*x^45 +72006964843*x^44 +20800791816*x^43 -64959622007*x^42 -16674723587*x^41 +8311317841*x^40 -41851983658*x^39 -10878840512*x^38 +60227329766*x^37 +71646302640*x^36 +111795917*x^35 -98969183331*x^34 -102248503015*x^33 +13126172584*x^32 +108338140330*x^31
%p +80553248220*x^30 -4243013616*x^29 -43486302952*x^28 -28181948095*x^27 -3688188878*x^26 +4299265271*x^25 +2263896509*x^24 +739802084*x^23 +845394966*x^22 +509931484*x^21 -127596363*x^20 -330548479*x^19 -74104054*x^18 +132481026*x^17 +79485565*x^16 +21861608*x^15 +12380793*x^14 +5359440*x^13 +161495*x^12 -1832730*x^11 -1066905*x^10 -274895*x^9 -73293*x^8 -3043*x^7 +5244*x^6 +1760*x^5 +358*x^4 +46*x^3 +29*x^2 +2*x -1):
%p a:= n-> coeff(series(gf, x, n+1), x, n):
%p seq(a(n), n=0..30);
%Y Column k=4 of A255256.
%Y Cf. A133357.
%K nonn,easy
%O 0,2
%A _Alois P. Heinz_, Feb 19 2015
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