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A206374
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a(n) = (7*4^n - 1)/3.
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5
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2, 9, 37, 149, 597, 2389, 9557, 38229, 152917, 611669, 2446677, 9786709, 39146837, 156587349, 626349397, 2505397589, 10021590357, 40086361429, 160345445717, 641381782869, 2565527131477, 10262108525909, 41048434103637, 164193736414549, 656774945658197
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OFFSET
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0,1
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COMMENTS
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First bisection of A062092 and A081253, second bisection of A097163. - Bruno Berselli, Feb 12 2012
Except a(0)=2, this is the 3rd row of table A178415. - Michel Marcus, Apr 13 2015
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Mike Warburton, Ulam-Warburton Automaton - Counting Cells with Quadratics, arXiv:1901.10565 [math.CO], 2019. See Table 1.
Index entries for linear recurrences with constant coefficients, signature (5,-4).
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FORMULA
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G.f.: (2-x)/(1-5*x+4*x^2). - Bruno Berselli, Feb 12 2012
a(n) = A083597(n)+1. - Bruno Berselli, Feb 12 2012
a(n) = 4*a(n-1)+1 for n>0, a(0)=2. - Bruno Berselli, Oct 22 2015
a(n) = 7*A002450(n) + 2. - Yosu Yurramendi, Jan 24 2017
A006666(a(n)) = 2*n+11 for n > 0. - Juan Miguel Barga Pérez, Jun 18 2020
a(n) = 5*a(n-1) - 4*a(n-2) for n >= 2. - Wesley Ivan Hurt, Jun 30 2020
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MATHEMATICA
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Table[(7(4^n) - 1)/3, {n, 0, 24}] (* Alonso del Arte, Feb 11 2012 *)
CoefficientList[Series[(2-x)/(1-5*x+4*x^2), {x, 0, 30}], x] (* or *) LinearRecurrence[{5, -4}, {2, 9}, 30] (* Vincenzo Librandi, Mar 20 2012 *)
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PROG
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(MAGMA) [(7*4^n-1)/3 : n in [0..30]];
(PARI) vector(20, n, (7*4^(n-1)-1)/3) \\ Derek Orr, Apr 12 2015
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CROSSREFS
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Cf. A002450, A006666, A072197; A002042 (first differences).
Sequence in context: A275425 A212386 A333883 * A037553 A178875 A012493
Adjacent sequences: A206371 A206372 A206373 * A206375 A206376 A206377
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KEYWORD
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nonn,easy
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AUTHOR
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Brad Clardy, Feb 07 2012
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STATUS
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approved
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