A250667 - OEIS

%I #11 Feb 06 2017 18:28:35

%S 1,1,1,1,1,1,1,1,1,1,13,27,43,61,81,103,127,153,181,211,484,967,1714,

%T 2785,4246,6169,8632,11719,15520,20131,30169,48753,80533,131499,

%U 209215,323073,484567,707587,1008733,1407649,2011933,2972524,4525434,7018281,10944565

%N Number of tilings of a 20 X n rectangle using 2n decominoes of shape I.

%H Alois P. Heinz, <a href="/A250667/b250667.txt">Table of n, a(n) for n = 0..1000</a>

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

%F G.f.: See Maple program.

%p gf:= -(x^45 -x^40 -4*x^36 -4*x^35 +3*x^31 +4*x^30 +6*x^27 +9*x^26 +6*x^25 -3*x^22 -6*x^21 -6*x^20 -4*x^18 -6*x^17 -6*x^16 -4*x^15 +x^13 +2*x^12 +3*x^11 +4*x^10 +x^9 +x^8 +x^7 +x^6 +x^5 -1) *(x-1)^9 *(x+1)^9 *(x^4+x^3+x^2+x+1)^9 *(x^4-x^3+x^2-x+1)^9 / (x^145 -x^140 -5*x^136 -14*x^135 +4*x^131 +14*x^130 +10*x^127 +60*x^126 +91*x^125 -6*x^122

%p -47*x^121 -91*x^120 -10*x^118 -105*x^117 -330*x^116 -364*x^115 +4*x^113 +61*x^112 +252*x^111 +364*x^110 +5*x^109 +95*x^108 +500*x^107 +1100*x^106 +1001*x^105 -x^104 -37*x^103 -280*x^102 -814*x^101 -1002*x^100 -45*x^99 -405*x^98 -1425*x^97 -2475*x^96 -2002*x^95 +9*x^94 +153*x^93 +765*x^92 +1760*x^91 +2011*x^90 +180*x^89 +1020*x^88

%p +2700*x^87 +3960*x^86 +3003*x^85 -36*x^84 -372*x^83 -1380*x^82 -2673*x^81 -3039*x^80 -420*x^79 -1680*x^78 -3570*x^77 -4620*x^76 -3432*x^75 +84*x^74 +588*x^73 +1722*x^72 +2904*x^71 +3516*x^70 +630*x^69 +1890*x^68 +3360*x^67 +3960*x^66 +3003*x^65 -126*x^64 -630*x^63 -1512*x^62 -2244*x^61 -3129*x^60 -630*x^59 -1470*x^58 -2250*x^57 -2475*x^56

%p -2011*x^55 +126*x^54 +462*x^53 +930*x^52 +1188*x^51 +2137*x^50 +420*x^49 +780*x^48 +1050*x^47 +1136*x^46 +1037*x^45 -84*x^44 -228*x^43 -390*x^42 -412*x^41 -1121*x^40 -180*x^39 -270*x^38 -379*x^37 -411*x^36 -418*x^35 +36*x^34 +72*x^33 +132*x^32 +98*x^31 +454*x^30 +45*x^29 +91*x^28

%p +114*x^27 +114*x^26 +127*x^25 -9*x^24 -22*x^23 -34*x^22 -9*x^21 -136*x^20 -14*x^19 -14*x^18 -14*x^17 -14*x^16 -23*x^15 +x^14 +x^13 +x^12 -8*x^11 +24*x^10 +x^5 +x -1):

%p a:= n-> coeff(series(gf, x, n+1), x, n):

%p seq(a(n), n=0..60);

%Y Column k=10 of A250662.

%Y Cf. A251079.

%K nonn,easy

%O 0,11

%A _Alois P. Heinz_, Nov 26 2014