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 A135440 a(n) = a(n-1) + 2a(n-2). 6
 -1, 4, 2, 10, 14, 34, 62, 130, 254, 514, 1022, 2050, 4094, 8194, 16382, 32770, 65534, 131074, 262142, 524290, 1048574, 2097154, 4194302, 8388610, 16777214, 33554434, 67108862, 134217730, 268435454, 536870914, 1073741822, 2147483650, 4294967294, 8589934594, 17179869182, 34359738370 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS First differences of A014551. - Reinhard Zumkeller, Jan 02 2013 It can be noticed that, once deprived of its first term, this is an "autosequence" of the second kind, whose companion of the first kind is A014113. - Jean-François Alcover, Aug 19 2022 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..1000 OEIS Wiki, Autosequence Index entries for linear recurrences with constant coefficients, signature (1,2). FORMULA From R. J. Mathar, Feb 19 2008: (Start) O.g.f.: -1/(2*x-1) - 2/(1+x). a(n) = 2^n - 2*(-1)^n. (End) a(n) = 2*A014551(n-1), n>0. - Paul Curtz, Jun 01 2011 E.g.f.: exp(2*x) - 2*exp(-x). - G. C. Greubel, Oct 14 2016 MATHEMATICA f[n_]:=2/(n+1); x=4; Table[x=f[x]; Numerator[x], {n, 0, 5!}] (* Vladimir Joseph Stephan Orlovsky, Mar 12 2010 *) LinearRecurrence[{1, 2}, {-1, 4}, 25] (* or *) Table[2^n - 2*(-1)^n, {n, 0, 25}] (* G. C. Greubel, Oct 14 2016 *) PROG (Haskell) a135440 n = a135440_list !! n a135440_list = zipWith (-) (tail a014551_list) a014551_list -- Reinhard Zumkeller, Jan 02 2013 CROSSREFS Sequence in context: A075086 A284782 A128781 * A215500 A188128 A336914 Adjacent sequences: A135437 A135438 A135439 * A135441 A135442 A135443 KEYWORD sign,easy AUTHOR Paul Curtz, Feb 18 2008 EXTENSIONS More terms from R. J. Mathar, Feb 19 2008 STATUS approved

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Last modified June 23 10:35 EDT 2024. Contains 373643 sequences. (Running on oeis4.)