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A250667
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Number of tilings of a 20 X n rectangle using 2n decominoes of shape I.
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3
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 13, 27, 43, 61, 81, 103, 127, 153, 181, 211, 484, 967, 1714, 2785, 4246, 6169, 8632, 11719, 15520, 20131, 30169, 48753, 80533, 131499, 209215, 323073, 484567, 707587, 1008733, 1407649, 2011933, 2972524, 4525434, 7018281, 10944565
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OFFSET
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0,11
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LINKS
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FORMULA
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G.f.: See Maple program.
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MAPLE
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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
-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
+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
-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
+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):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..60);
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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