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A236582
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The number of tilings of an 8 X n floor with 1 X 4 tetrominoes.
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6
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1, 1, 1, 1, 7, 15, 25, 37, 100, 229, 454, 811, 1732, 3777, 7858, 15339, 31273, 65536, 136600, 276535, 562728, 1159942, 2400783, 4918159, 10052140, 20627526, 42480474, 87254743, 178855138, 366854368
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OFFSET
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0,5
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COMMENTS
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Tilings are counted irrespective of internal symmetry: Tilings that match each other after rotations and/or reflections are counted with their multiplicity.
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LINKS
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FORMULA
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G.f.: p(x)/q(x) with polynomials p and q defined in the Maple code.
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MAPLE
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p := (1-x)^3*(x+1)^3*(x^2+1)^3*(x^6-x^4-x^3-x^2+1) ;
q := -x^2 -13*x^10 -5*x^18 +8*x^6 -x -x^20 -9*x^4 +16*x^8 -13*x^12 -2*x^19 +1 +10*x^14 +5*x^7 +6*x^15 -6*x^11 +x^22 +6*x^16 +x^17 +2*x^5 -2*x^13 ;
taylor(p/q, x=0, 30) ;
gfun[seriestolist](%) ;
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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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