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A288170
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a(n) = 3*a(n-1) - a(n-2) - 4*a(n-3) + 2*a(n-4) for n >= 4, where a(0) = 2, a(1) = 4, a(2) = 8, a(3) = 16, a(4) = 34, a(5) = 70 .
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2
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2, 4, 8, 16, 34, 70, 144, 292, 590, 1186, 2380, 4768, 9546, 19102, 38216, 76444, 152902, 305818, 611652, 1223320, 2446658, 4893334, 9786688, 19573396, 39146814, 78293650, 156587324, 313174672, 626349370, 1252698766, 2505397560, 5010795148, 10021590326
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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->000, starting with 00; see A288167.
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LINKS
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FORMULA
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a(n) = 3*a(n-1) - a(n-2) - 4*a(n-3) + 2*a(n-4) for n >= 4, where a(0) = 2, a(1) = 4, a(2) = 8, a(3) = 16, a(4) = 34, a(5) = 70 .
G.f.: 2 + (2*x*(-2 + 2*x + 2*x^2 - 3*x^3))/((-1 + x)^2*(-1 + x + 2*x^2)).
a(n) = (3 + (-1)^n + 7*2^(1+n) - 6*n) / 6 for n>0. - Colin Barker, Sep 29 2017
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MATHEMATICA
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Join[{2}, LinearRecurrence[{3, -1, -3, 2}, {4, 8, 16, 34}, 40]]
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PROG
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(PARI) Vec(2*(1 - x - x^2 + x^3 + x^4) / ((1 - x)^2*(1 + x)*(1 - 2*x)) + O(x^30)) \\ 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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