A270064 - OEIS

%I #8 Feb 06 2017 12:31:22

%S 1,3,45,590,7517,96176,1238818,15913695,204383373,2626057921,

%T 33738191906,433438712623,5568545948434,71541033899738,

%U 919110571684493,11808116466700575,151702772808195855,1948975423808006804,25039128916718657873,321685935180001027054

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

%H Alois P. Heinz, <a href="/A270064/b270064.txt">Table of n, a(n) for n = 0..900</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Tromino">Tromino</a>

%F 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

%F +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)

%F / (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

%F +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).

%Y Column k=4 of A270061.

%K nonn,easy

%O 0,2

%A _Alois P. Heinz_, Mar 09 2016