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A080674
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a(n) = (4/3)*(4^n - 1).
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17
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0, 4, 20, 84, 340, 1364, 5460, 21844, 87380, 349524, 1398100, 5592404, 22369620, 89478484, 357913940, 1431655764, 5726623060, 22906492244, 91625968980, 366503875924, 1466015503700, 5864062014804, 23456248059220, 93824992236884, 375299968947540, 1501199875790164
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OFFSET
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0,2
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COMMENTS
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a(n) is the number of steps which are made when generating all n-step random walks that begin in a given point P on a two-dimensional square lattice. To make one step means to move along one edge on the lattice. - Pawel P. Mazur (Pawel.Mazur(AT)pwr.wroc.pl), Mar 10 2005
Conjectured to be the number of integers from 0 to (10^n)-1 that lack 0, 1, 2, 3, 4 and 5 as a digit. - Alexandre Wajnberg, Apr 25 2005
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LINKS
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FORMULA
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a(n) = Sum_{i = 1..n} 4^i. - Adam McDougall (mcdougal(AT)stolaf.edu), Sep 29 2004
a(n) = 5*a(n-1) - 4*a(n-2).
G.f.: 4*x / ((x-1)*(4*x-1)). (End)
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MATHEMATICA
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LinearRecurrence[{5, -4}, {0, 4}, 40] (* Harvey P. Dale, May 05 2018 *)
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PROG
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(PARI) vector(100, n, n--; (4/3)*(4^n-1)) \\ Altug Alkan, Oct 11 2015
(PARI) Vec(4*x/((x-1)*(4*x-1)) + O(x^40)) \\ Colin Barker, Oct 12 2015
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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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