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A209528
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The number of length n ternary sequences in which no symbol appears exactly once.
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1
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1, 0, 3, 3, 21, 63, 243, 969, 3657, 12987, 43959, 143685, 458109, 1435047, 4439451, 13612257, 41474577, 125798643, 380343519, 1147320285, 3455328261, 10394294175, 31242648963, 93853773369, 281825558361, 846030320043, 2539248584583, 7620161669109
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OFFSET
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0,3
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LINKS
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Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (10,-40,82,-91,52,-12).
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FORMULA
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E.g.f.: (exp(x)-x)^3.
For n>3: a(n) = 3^n - 3*n*2^(n-1) + 3*n*(n-1).
G.f.: -(72*x^9 -312*x^8 +546*x^7 -492*x^6 +325*x^5 -202*x^4 +109*x^3 -43*x^2 +10*x -1) / ((x -1)^3*(2*x -1)^2*(3*x -1)). - Colin Barker, Nov 30 2014
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EXAMPLE
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a(2)=3 because we have (letting our alphabet be {0,1,2}) three length two sequences: (0,0), (1,1), (2,2).
a(3)=3 because we have: (0,0,0), (1,1,1), (2,2,2).
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MATHEMATICA
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nn=20; a=Exp[x]-x; Range[0, nn]! CoefficientList[Series[a^3, {x, 0, nn}], x]
LinearRecurrence[{10, -40, 82, -91, 52, -12}, {1, 0, 3, 3, 21, 63, 243, 969, 3657, 12987}, 30] (* Harvey P. Dale, Aug 20 2015 *)
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PROG
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(PARI) Vec(-(72*x^9 -312*x^8 +546*x^7 -492*x^6 +325*x^5 -202*x^4 +109*x^3 -43*x^2 +10*x -1) / ((x -1)^3*(2*x -1)^2*(3*x -1)) + O(x^100)) \\ Colin Barker, Nov 30 2014
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CROSSREFS
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Cf. A130102.
Sequence in context: A172485 A230647 A130723 * A214778 A180754 A224091
Adjacent sequences: A209525 A209526 A209527 * A209529 A209530 A209531
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KEYWORD
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nonn,easy
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AUTHOR
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Geoffrey Critzer, Mar 20 2012
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STATUS
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approved
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