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1, 2, 10, 62, 370, 2102, 11530, 61742, 325090, 1690982, 8717050, 44633822, 227363410, 1153594262, 5835080170, 29443836302, 148292923330, 745759583942, 3745977788890, 18798608421182, 94267920012850, 472439111692022
(list;
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history;
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..21.
Index entries for linear recurrences with constant coefficients, signature (10,-29,20).
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FORMULA
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G.f.: 1/(1-5*x)-1/(1-4*x)+1/(1-x). E.g.f.: e^(5*x)-e^(4*x)+e^x.
a(n)=9*a(n-1)-20*a(n-2)+12 with a(0)=1, a(1)=2 - Vincenzo Librandi, Jul 21 2010
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MATHEMATICA
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Table[5^n-4^n+1, {n, 0, 40}]
(* Vladimir Joseph Stephan Orlovsky, Feb 15 2011*)
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PROG
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(PARI) a(n)=5^n-4^n+1 \\ Charles R Greathouse IV, Jun 11 2015
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CROSSREFS
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Cf. A054401, which is essentially a(n) - 2. Also A155588, A155589, A155590, A155592, A155593, A155594, A155595, A155596, A155597, A155598, A155599, A155600, A155601, A155622, A155623, A155624, A155625.
Sequence in context: A277472 A052600 A183958 * A092165 A304443 A243034
Adjacent sequences: A155623 A155624 A155625 * A155627 A155628 A155629
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KEYWORD
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nonn,easy
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AUTHOR
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Mohammad K. Azarian, Jan 29 2009
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STATUS
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approved
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