A270064 Number of tilings of a 4 X n rectangle using monominoes and trominoes of any shape.

1, 3, 45, 590, 7517, 96176, 1238818, 15913695, 204383373, 2626057921, 33738191906, 433438712623, 5568545948434, 71541033899738, 919110571684493, 11808116466700575, 151702772808195855, 1948975423808006804, 25039128916718657873, 321685935180001027054

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..900

Wikipedia, Tromino

Formula

G.f.: -(x^42 -2*x^41 +3*x^40 -45*x^39 +75*x^38 -104*x^37 +788*x^36 -1328*x^35 +1326*x^34 -8174*x^33 +13318*x^32 -9055*x^31 +51980*x^30 -68274*x^29 +18138*x^28 -163965*x^27 +144209*x^26 +50099*x^25 +307359*x^24 -237066*x^23 -88998*x^22 -420220*x^21 +288839*x^20

+56875*x^19 +263379*x^18 -179966*x^17 +19258*x^16 -47380*x^15 +99349*x^14 -28851*x^13 -16616*x^12 -21781*x^11 +15041*x^10 -705*x^9 -2136*x^8 -1268*x^7 +2193*x^6 +558*x^5 -149*x^4 -187*x^3 -25*x^2 -4*x +1)

/ (x^45 -2*x^44 +4*x^43 -58*x^42 +90*x^41 -162*x^40 +1072*x^39 -1745*x^38 +1906*x^37 -10656*x^36 +21746*x^35 -17639*x^34 +90014*x^33 -190035*x^32 +136443*x^31 -516421*x^30 +828239*x^29 -326624*x^28 +1290743*x^27 -1284720*x^26 -519116*x^25 -1599589*x^24 +1444541*x^23 +956723*x^22

+2264534*x^21 -1759452*x^20 -691070*x^19 -1308065*x^18 +953491*x^17 +192415*x^16 +204107*x^15 -475505*x^14 +77942*x^13 +133756*x^12 +68320*x^11 -73312*x^10 -9470*x^9 +10934*x^8 +4282*x^7 -4428*x^6 -1244*x^5 +386*x^4 +315*x^3 +49*x^2 +7*x -1).

Crossrefs

Column k=4 of A270061.

Sequence in context: A360716 A060242 A271236 * A141445 A076140 A131568

Adjacent sequences: A270061 A270062 A270063 * A270065 A270066 A270067

Keyword

nonn,easy

Author

Alois P. Heinz, Mar 09 2016

Status

approved