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A084222
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a(n) = -2*a(n-1) + 3*a(n-2), with a(0)=1, a(1)=2.
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8
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1, 2, -1, 8, -19, 62, -181, 548, -1639, 4922, -14761, 44288, -132859, 398582, -1195741, 3587228, -10761679, 32285042, -96855121, 290565368, -871696099, 2615088302, -7845264901, 23535794708, -70607384119, 211822152362, -635466457081, 1906399371248
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = (5-(-3)^n)/4.
G.f.: (1+4*x)/((1-x)*(1+3*x)).
E.g.f.: (5*exp(x)-exp(-3*x))/4.
For n > 1, abs(a(n) - a(n+1)) = 3^n. - Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jul 15 2003; corrected by Philippe Deléham, Dec 16 2007
a(n) = 9*a(n-2) - 10 with a(0) = 1 and a(1) = 2. - Philippe Deléham, Feb 24 2014
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MATHEMATICA
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CoefficientList[Series[(1 + 4 x)/((1 - x) (1 + 3 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Feb 26 2014 *)
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PROG
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(PARI) a(n) = (5-(-3)^n)/4; \\ Joerg Arndt, Jul 14 2013
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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STATUS
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approved
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