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A296965
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Expansion of x*(1 - x + 2*x^2) / ((1 - x)*(1 - 2*x)).
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2
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0, 1, 2, 6, 14, 30, 62, 126, 254, 510, 1022, 2046, 4094, 8190, 16382, 32766, 65534, 131070, 262142, 524286, 1048574, 2097150, 4194302, 8388606, 16777214, 33554430, 67108862, 134217726, 268435454, 536870910, 1073741822, 2147483646, 4294967294, 8589934590, 17179869182
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OFFSET
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0,3
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COMMENTS
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a(n) = A000225(n)-1, a(0)=0, a(1)=1. Number of quasilinear weak orderings R on {1,...,n} that are weakly single-peaked w.r.t. the total ordering 1<...<n and for which {1,...,n} has exactly one maximal element for the quasilinear weak ordering R.
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LINKS
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FORMULA
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G.f.: x*(1 - x + 2*x^2) / ((1 - x)*(1 - 2*x)).
a(n) = 2^n - 2 for n>1.
a(n) = 3*a(n-1) - 2*a(n-2) for n>3. (End)
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MATHEMATICA
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CoefficientList[Series[x (1 - x + 2 x^2)/((1 - x) (1 - 2 x)), {x, 0, 33}], x] (* or *)
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PROG
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(PARI) concat(0, Vec(x*(1 - x + 2*x^2) / ((1 - x)*(1 - 2*x)) + O(x^40))) \\ Colin Barker, Dec 22 2017
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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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