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A055195
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Number of 3-covers of an unlabeled n-set.
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2
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1, 9, 29, 72, 154, 294, 522, 877, 1406, 2172, 3255, 4746, 6763, 9445, 12953, 17480, 23254, 30528, 39604, 50823, 64568, 81276, 101443, 125610, 154395, 188479, 228611, 275622, 330432, 394032, 467524, 552103, 649064, 759818, 885901
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OFFSET
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2,2
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COMMENTS
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Covers are defined in proper sense, i.e. without empty sets or multiple sets.
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LINKS
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Eric Weisstein's World of Mathematics, Covers
Index entries for linear recurrences with constant coefficients, signature (3,-1,-3,-1,3,6,-6,-3,1,3,1,-3,1).
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FORMULA
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G.f.: x^2*(x^11-x^10-3*x^9+4*x^7+6*x^6-3*x^5-5*x^4-3*x^3+3*x^2+6*x+1)/((1-x^3)^2*(1-x^2)^2*(1-x)^3).
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MATHEMATICA
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Drop[CoefficientList[Series[x^2(x^11-x^10-3x^9+4x^7+6x^6-3x^5-5x^4-3x^3+ 3x^2+6x+1)/ ((1-x^3)^2(1-x^2)^2(1-x)^3), {x, 0, 40}], x], 2] (* or *) LinearRecurrence[ {3, -1, -3, -1, 3, 6, -6, -3, 1, 3, 1, -3, 1}, {1, 9, 29, 72, 154, 294, 522, 877, 1406, 2172, 3255, 4746, 6763}, 40] (* Harvey P. Dale, Jul 18 2021 *)
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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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EXTENSIONS
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STATUS
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approved
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