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 A154691 Expansion of (1+x+x^2) / ((1-x-x^2)*(1-x)). 5
 1, 3, 7, 13, 23, 39, 65, 107, 175, 285, 463, 751, 1217, 1971, 3191, 5165, 8359, 13527, 21889, 35419, 57311, 92733, 150047, 242783, 392833, 635619, 1028455, 1664077, 2692535, 4356615, 7049153, 11405771, 18454927, 29860701, 48315631, 78176335 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (2,0,-1). FORMULA a(n+1) - a(n) = A006355(n+3) = A055389(n+3). a(n) = A066629(n-1) + A066629(n). a(n) = A006355(n+4) - 3 = A078642(n+1) - 3. a(n+1) = a(n) + 2*A000045(n+2). - Reinhard Zumkeller, Nov 17 2013 From Colin Barker, Feb 01 2017: (Start) a(n) = -3 + (2^(1-n)*((1-r)^n*(-2+r) + (1+r)^n*(2+r))) / r where r=sqrt(5). a(n) = 2*a(n-1) - a(n-3) for n>2. (End) MAPLE A154691 := proc(n) coeftayl( (1+x+x^2)/(1-x-x^2)/(1-x), x=0, n) ; end proc: MATHEMATICA Fibonacci[Range[3, 5! ]]*2-3 (* Vladimir Joseph Stephan Orlovsky, Mar 19 2010 *) CoefficientList[Series[(1 + x + x^2)/((1 - x - x^2)(1 - x)), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 18 2012 *) PROG (Haskell) a154691 n = a154691_list !! n a154691_list = 1 : zipWith (+)                    a154691_list (drop 2 \$ map (* 2) a000045_list) -- Reinhard Zumkeller, Nov 17 2013 (PARI) Vec((1+x+x^2) / ((1-x-x^2)*(1-x)) + O(x^60)) \\ Colin Barker, Feb 01 2017 CROSSREFS Cf. A006355, A055389, A066629, A078642. Cf. A001595, A166863. Sequence in context: A136851 A155339 A122886 * A306902 A227121 A078447 Adjacent sequences:  A154688 A154689 A154690 * A154692 A154693 A154694 KEYWORD easy,nonn AUTHOR R. J. Mathar, Jan 14 2009 STATUS approved

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Last modified January 22 19:39 EST 2020. Contains 331153 sequences. (Running on oeis4.)