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 A045873 A006496/2. 12
 0, 1, 2, -1, -12, -19, 22, 139, 168, -359, -1558, -1321, 5148, 16901, 8062, -68381, -177072, -12239, 860882, 1782959, -738492, -10391779, -17091098, 17776699, 121008888, 153134281, -298775878, -1363223161, -1232566932 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Partial sums of A006495. - Paul Barry, Mar 16 2006 This is the Lucas U(P=2,Q=5) sequence. - R. J. Mathar, Oct 24 2012 With different signs, 0, 1, -2, -1, 12, -19, -22, 139, -168, -359, 1558,.. we obtain the Lucas U(-2,5) sequence. - R. J. Mathar, Jan 08 2013 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..500 Wikipedia, Lucas sequence Index entries for linear recurrences with constant coefficients, signature (2,-5). FORMULA Contribution from Paul Barry, Sep 20 2003: (Start) G.f.: x/(1-2x+5x^2); E.g.f.: exp(x)sin(2x)/2; a(n) = 2*a(n-1)-5*a(n-2), a(0)=0, a(1)=1; a(n) = ((1+2i)^n-(1-2i)^n)/(4i), where i=sqrt(-1); a(n) = Im{(1+2i)^n/2}; a(n) = sum{k=0..floor(n/2), C(n, 2k+1)(-4)^k}. (End) a(n+1) = sum{k=0..n, C(k,n-k)2^k*(-5/2)^(n-k)}. - Paul Barry, Mar 16 2006 G.f.: 1/(4*x - 1/G(0)) where G(k) =  1 - (k+1)/(1 - x/(x - (k+1)/G(k+1) )); (recursively defined continued fraction). - Sergei N. Gladkovskii, Dec 06 2012 G.f.: Q(0)*x/2, where Q(k) = 1 + 1/(1 - x*(4*k+2 - 5*x)/( x*(4*k+4 - 5*x) + 1/Q(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Aug 30 2013 MATHEMATICA Join[{a=0, b=1}, Table[c=2*b-5*a; a=b; b=c, {n, 100}]] (* Vladimir Joseph Stephan Orlovsky, Jan 17 2011*) PROG (Sage) [lucas_number1(n, 2, 5) for n in xrange(0, 29)] # [From Zerinvary Lajos, Apr 23 2009] (PARI) concat(0, Vec(1/(1-2*x+5*x^2)+O(x^99))) \\ Charles R Greathouse IV, Dec 22 2011 CROSSREFS Cf. A084102, A088136, A088137, A088139. a(n)^2 = A094423(n). Sequence in context: A151508 A164826 A055392 * A265022 A110060 A061081 Adjacent sequences:  A045870 A045871 A045872 * A045874 A045875 A045876 KEYWORD sign,easy AUTHOR EXTENSIONS More terms from Paul Barry, Sep 20 2003 STATUS approved

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