A255255 Number of 2-colorings of a 4 X n rectangle such that no nontrivial subsquare has monochromatic corners.

1, 16, 178, 1498, 10980, 85138, 655090, 5115398, 39914386, 312388874, 2436283602, 18994966598, 148059349634, 1154792660474, 9007078544234, 70254124462638, 547921292697778, 4273303250042966, 33327954035543034, 259932116476519958, 2027268764564330754

Offset: 0

Author

Alois P. Heinz, Feb 19 2015

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Column k=4 of A255256.

Cf. A133357.

Programs

Maple

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 [phone]*x^70 [phone]*x^69 -56935120*x^68 -320396192*x^67 [phone]*x^66 [phone]*x^65 -800166640*x^64 [phone]*x^63 -3217094764*x^62 -2931282696*x^61 [phone]*x^60 -25189807228*x^59 [phone]*x^58 [phone]*x^57 -79785446783*x^56 [phone]*x^55 [phone]*x^54 -184157650742*x^53 [phone]*x^52 [phone]*x^51 -205358037404*x^50
[phone]*x^49 -54179691207*x^48 -58933050614*x^47 -72350094400*x^46 [phone]*x^45 [phone]*x^44 -31136120454*x^43 [phone]*x^42 [phone]*x^41 -259850982087*x^40 -250072129598*x^39 -106581496436*x^38 [phone]*x^37 [phone]*x^36 [phone]*x^35 -275403863093*x^34 -334505242945*x^33 -114680900580*x^32 [phone]*x^31 [phone]*x^30 [phone]*x^29
[phone]*x^28 -93783726011*x^27 -117305441726*x^26 -63470276869*x^25 -4776176481*x^24 [phone]*x^23 [phone]*x^22 [phone]*x^21 [phone]*x^20 [phone]*x^19 -720102442*x^18 -787824686*x^17 -195158015*x^16 [phone]*x^15 [phone]*x^14 +9512482*x^13 [phone]*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) /
(-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 [phone]*x^65 [phone]*x^64 -287868964*x^63 [phone]*x^62 -345759930*x^61 [phone]*x^60 [phone]*x^59 -4711903718*x^58 [phone]*x^57 [phone]*x^56 -23454331276*x^55 [phone]*x^54
[phone]*x^53 -42633850200*x^52 [phone]*x^51 [phone]*x^50 -59350410523*x^49 [phone]*x^48 [phone]*x^47 -36411691280*x^46 [phone]*x^45 [phone]*x^44 [phone]*x^43 -64959622007*x^42 -16674723587*x^41 [phone]*x^40 -41851983658*x^39 -10878840512*x^38 [phone]*x^37 [phone]*x^36 [phone]*x^35 -98969183331*x^34 -102248503015*x^33 [phone]*x^32 [phone]*x^31
[phone]*x^30 -4243013616*x^29 -43486302952*x^28 -28181948095*x^27 -3688188878*x^26 [phone]*x^25 [phone]*x^24 [phone]*x^23 [phone]*x^22 [phone]*x^21 -127596363*x^20 -330548479*x^19 -74104054*x^18 [phone]*x^17 [phone]*x^16 [phone]*x^15 [phone]*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):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..30);

Formula

G.f.: see Maple program.