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A288206
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a(n) = 3*a(n-1) - a(n-2) - 3*a(n-3) + 2*a(n-4), where a(0) = 2, a(1) = 4, a(2) = 8, a(3) = 18.
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2
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2, 4, 8, 18, 38, 80, 164, 334, 674, 1356, 2720, 5450, 10910, 21832, 43676, 87366, 174746, 349508, 699032, 1398082, 2796182, 5592384, 11184788, 22369598, 44739218, 89478460, 178956944, 357913914, 715827854, 1431655736, 2863311500, 5726623030, 11453246090
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OFFSET
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0,1
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COMMENTS
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Conjecture: a(n) is the number of letters (0's and 1's) in the n-th iteration of the mapping 00->0010, 1->010, starting with 00; see A288203.
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LINKS
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FORMULA
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a(n) = 3*a(n-1) - a(n-2) - 3*a(n-3) + 2*a(n-4), where a(0) = 2, a(1) = 4, a(2) = 8, a(3) = 18.
G.f.: -((2*(1 - x - x^2 + 2*x^3))/((-1 + x)^2*(-1 + x + 2*x^2))).
a(n) = (-3 + (-1)^(1+n) + 2^(4+n) - 6*n) / 6. - Colin Barker, Sep 29 2017
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MATHEMATICA
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LinearRecurrence[{3, -1, -3, 2}, {2, 4, 8, 18}, 40]
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PROG
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(PARI) Vec(2*(1 - x - x^2 + 2*x^3) / ((1 - x)^2*(1 + x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, Sep 29 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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