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A302757
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a(n) is the smallest number whose greedy representation as a sum of terms of A126684 uses n terms.
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1
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1, 3, 13, 55, 225, 907, 3637, 14559, 58249, 233011, 932061, 3728263, 14913073, 59652315, 238609285, 954437167, 3817748697, 15270994819, 61083979309, 244335917271, 977343669121, 3909374676523, 15637498706133, 62549994824575, 250199979298345, 1000799917193427
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OFFSET
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1,2
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COMMENTS
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A126684 is described as the fastest-growing sequence such that every nonnegative integer is the sum of two of its terms. However, if one uses a greedy algorithm to find a representation as a sum of its terms, the length of the representation will typically be more than two. This sequence gives the numbers whose greedy representations have record-setting lengths. For example, a(3) = 13 because (although 13 = 8 + 5, a representation as a sum of two terms of A126684) the greedy algorithm represents it as the three-term sum 13 = 10 + 2 + 1.
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LINKS
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FORMULA
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a(n) = 4*a(n-1) + 2*n - 5.
G.f.: x*(1 - 3*x + 4*x^2) / ((1 - x)^2*(1 - 4*x)).
a(n) = (7 + 2^(1+2*n) - 6*n) / 9.
a(n) = 6*a(n-1) - 9*a(n-2) + 4*a(n-3) for n>3.
(End)
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MATHEMATICA
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Fold[Append[#1, 4 Last[#1] + 2 #2 - 5] &, {1}, Range[2, 25]] (* Michael De Vlieger, Apr 12 2018 *)
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PROG
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(PARI) Vec(x*(1 - 3*x + 4*x^2) / ((1 - x)^2*(1 - 4*x)) + O(x^60)) \\ Colin Barker, Apr 13 2018
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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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