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A246313
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G.f.: (-1+6*x)/(1-3*x-2*x^2).
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1
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-1, 3, 7, 27, 95, 339, 1207, 4299, 15311, 54531, 194215, 691707, 2463551, 8774067, 31249303, 111296043, 396386735, 1411752291, 5028030343, 17907595611, 63778847519, 227151733779, 809012896375, 2881342156683, 10262052262799, 36548841101763, 130170627830887, 463609565696187, 1651169952750335
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OFFSET
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0,2
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COMMENTS
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Encountered during the analysis of a certain cellular automaton.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,2).
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FORMULA
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a(n) = 3*a(n-1) + 2*a(n-2) with a(0)=-1, a(1)=3.
a(n) = -(17+9*sqrt(17))/34*(3/2-sqrt(17)/2)^n+(-17+9*sqrt(17))/34*(3/2+sqrt(17)/2)^n. For n >= 3, a(n) = round(-17+9*sqrt(17))/34*(3/2+sqrt(17)/2)^n). - Robert Israel, Aug 27 2014
a(n) = 6*A007482(n-1)+A007482(n). - R. J. Mathar, Feb 27 2019
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MAPLE
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a:= LRETools[REtoproc](a(n)=3*a(n-1)+2*a(n-2), a(n), {a(0)=-1, a(1)=3}):
seq(a(i), i=0..100); # Robert Israel, Aug 27 2014
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MATHEMATICA
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CoefficientList[Series[(6 x - 1)/(1 - 3 x - 2 x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Aug 27 2014 *)
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PROG
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(MAGMA) I:=[-1, 3]; [n le 2 select I[n] else 3*Self(n-1)+2*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Aug 27 2014
(PARI) Vec((-1+6*x)/(1-3*x-2*x^2)+O(x^99)) \\ Charles R Greathouse IV, Sep 02 2014
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CROSSREFS
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Sequence in context: A081562 A216174 A260464 * A003083 A062795 A062363
Adjacent sequences: A246310 A246311 A246312 * A246314 A246315 A246316
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KEYWORD
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sign,easy
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AUTHOR
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N. J. A. Sloane, Aug 26 2014
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STATUS
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approved
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