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A168609
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a(n) = 3^n + 4.
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3
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5, 7, 13, 31, 85, 247, 733, 2191, 6565, 19687, 59053, 177151, 531445, 1594327, 4782973, 14348911, 43046725, 129140167, 387420493, 1162261471, 3486784405, 10460353207, 31381059613, 94143178831, 282429536485, 847288609447
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history;
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OFFSET
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0,1
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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 (4,-3).
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FORMULA
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a(n) = 3*a(n-1) - 8, with n>0, a(0)=5.
G.f.: (5 - 13*x)/((1-x)*(1-3 x)). - Vincenzo Librandi, May 13 2014
a(n) = 4*a(n-1) - 3*a(n-2) for n>1. - Vincenzo Librandi, May 13 2014
E.g.f.: exp(3*x) + 4*exp(x). - G. C. Greubel, Jul 27 2016
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EXAMPLE
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a(1)=3*5-8=7; a(2)=3*7-8=13; a(3)=3*13-8=31.
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MATHEMATICA
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Table[3^n + 4, {n, 0, 50}] (* Vladimir Joseph Stephan Orlovsky, May 19 2011 *)
CoefficientList[Series[(5 - 13 x)/((1 - x) (1 - 3 x)), {x, 0, 30}], x] (* Vincenzo Librandi, May 13 2014 *)
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PROG
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(MAGMA) [3^n+4: n in [0..30]]; // Vincenzo Librandi, May 13 2014
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CROSSREFS
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Cf. A034472, A168607, A168610, A178674.
Sequence in context: A141191 A101782 A288889 * A266951 A102903 A294064
Adjacent sequences: A168606 A168607 A168608 * A168610 A168611 A168612
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KEYWORD
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nonn,easy
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AUTHOR
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Vincenzo Librandi, Dec 01 2009
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EXTENSIONS
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Formula and examples edited to use correct offset by Jon E. Schoenfield, Jun 19 2010
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STATUS
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approved
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