Search: id:A098149
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%I A098149
%S A098149 1,1,4,11,29,76,199,521,1364,3571,9349,24476,64079,167761,439204,
%T A098149 1149851,3010349,7881196,20633239,54018521,141422324,370248451,
%U A098149 969323029,2537720636,6643838879,17393796001,45537549124,119218851371
%V A098149 -1,-1,4,-11,29,-76,199,-521,1364,-3571,9349,-24476,64079,-167761,439204,
               -1149851,
%W A098149 3010349,-7881196,20633239,-54018521,141422324,-370248451,969323029,-2537720636,
%X A098149 6643838879,-17393796001,45537549124,-119218851371
%N A098149 a(0)=-1, a(1)=-1, a(n)=-3*a(n-1)-a(n-2) for n>1.
%C A098149 Sequence relates bisections of Lucas and Fibonacci numbers.
%C A098149 2*a(n) + A098150(n) = 8*(-1)^(n+1)*A001519(n) - (-1)^(n+1)*A005248(n+1). 
               Apparently, if (z(n)) is any sequence of integers (not all zero) 
               satisfying the formula z(n) = 2(z(n-2) - z(n-1)) + z(n-3) then |z(n+1)/
               z(n)| -> golden ratio phi + 1 = (3+sqrt(5))/2
%H A098149 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A098149 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%F A098149 G.f.: -(1+4*x)/(1+3*x+x^2).
%F A098149 a(n) = 2(a(n-2) - a(n-1)) + a(n-3), with a(0) = a(1) = -1 and a(2) = 
               4.
%F A098149 -a(n+1)= Sum_{k, 0<=k<=n}(-5)^k*Binomial(n+k,n-k)= Sum_{k, 0<=k<=n}(-5)^k*A085478(n,
               k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 28 2006
%F A098149 a(n)=-(1/2)*[(-3/2)-(1/2)*sqrt(5)]^n+(1/2)*[(-3/2)-(1/2)*sqrt(5)]^n*sqrt(5)-(1/
               2)*[(-3/2)+(1/2) *sqrt(5)]^n*sqrt(5)-(1/2)*[(-3/2)+(1/2)*sqrt(5)]^n, 
               with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Nov 19 2008]
%t A098149 a[0] = a[1] = -1; a[2] = 4; a[n_] := a[n] = 2(a[n - 2] - a[n - 1]) + 
               a[n - 3]; Table[ a[n], {n, 0, 27}] (from Robert G. Wilson v Sep 01 
               2004)
%Y A098149 Cf. A098150, A001519, A005248.
%Y A098149 Sequence in context: A027970 A027972 A002878 this_sequence A124861 A110579 
               A084378
%Y A098149 Adjacent sequences: A098146 A098147 A098148 this_sequence A098150 A098151 
               A098152
%K A098149 easy,sign
%O A098149 0,3
%A A098149 Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Aug 29 2004
%E A098149 More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 1 2004
%E A098149 Simpler definition and generating function from Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Nov 19 2006

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