Search: id:A075193
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%I A075193
%S A075193 1,3,4,7,11,18,29,47,76,123,199,322,521,843,1364,2207,3571,5778,9349,15127,
%T A075193 24476,39603,64079,103682,167761,271443,439204,710647,1149851,1860498,
               3010349,
%U A075193 4870847,7881196,12752043,20633239,33385282,54018521,87403803,141422324
%V A075193 1,-3,4,-7,11,-18,29,-47,76,-123,199,-322,521,-843,1364,-2207,3571,-5778,
               9349,-15127,
%W A075193 24476,-39603,64079,-103682,167761,-271443,439204,-710647,1149851,-1860498,
               3010349,
%X A075193 -4870847,7881196,-12752043,20633239,-33385282,54018521,-87403803,141422324
%N A075193 "Inverted" Lucas numbers (see Comments).
%C A075193 The g.f. is obtained inserting 1/x into the g.f. of Lucas sequence and 
               dividing by x. The closed form is a(n)=(-1)^n*a^(n+1)+(-1)^n*b^(n+1), 
               where a=golden ratio and b=1-a, so that a(n)=(-1)^n*L(n+1), L(n)=Lucas 
               numbers.
%H A075193 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A075193 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%F A075193 a(n)=-a(n-1)+a(n-2), a(0)=1, a(1)=-3. G.f.: (1-2x)/(1+x-x^2).
%F A075193 a(n) = term (1,1) in the 1x2 matrix [1,-2] . [-1,1; 1,0]^n. [From Alois 
               P. Heinz (heinz(AT)hs-heilbronn.de), Jul 31 2008]
%p A075193 (Maple) a := n -> (Matrix([[1,-2]]).Matrix([[-1,1], [1,0]])^(n))[1,1]; 
               seq (a(n), n=0..38); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), 
               Jul 31 2008]
%t A075193 CoefficientList[Series[(1 - 2z)/(1 + z - z^2), {z, 0, 40}], z]
%Y A075193 Cf. A000032.
%Y A075193 Sequence in context: A100581 A093090 A000204 this_sequence A042433 A024319 
               A041209
%Y A075193 Adjacent sequences: A075190 A075191 A075192 this_sequence A075194 A075195 
               A075196
%K A075193 easy,sign
%O A075193 0,2
%A A075193 Mario Catalani (mario.catalani(AT)unito.it), Sep 07 2002

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