Search: id:A099372
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%I A099372
%S A099372 0,1,81,6724,558009,46308025,3843008064,318923361289,26466795978921,
%T A099372 2196425142889156,182276820063821025,15126779640154255921,
%U A099372 1255340433312739420416,104178129185317217638609
%N A099372 Squares of A099371(n) (generalized Fibonacci).
%C A099372 See the comment in A099279. This is example a=9.
%H A099372 <a href="Sindx_Ch.html#Cheby">Index entries for sequences related to 
               Chebyshev polynomials.</a>
%F A099372 a(n)= A099371(n)^2.
%F A099372 a(n)= 82*a(n-1) + 82*a(n-2) - a(n-3), n>=3; a(0)=0, a(1)=1, a(2)=81.
%F A099372 a(n)= 83*a(n-1) - a(n-2) - 2*(-1)^n, n>=2; a(0)=0, a(1)=1.
%F A099372 a(n)= 2*(T(n, 83/2)-(-1)^n)/85 with twice the Chebyshev's polynomials 
               of the first kind: 2*T(n, 83/2)=A099373(n).
%F A099372 G.f.: x*(1-x)/((1-83*x+x^2)*(1+x)) = x*(1-x)/(1-82*x-82*x^2+x^3).
%F A099372 a(n)=-(2/85)*(-1)^n+(1/85)*[83/2+(9/2)*sqrt(85)]^n+(1/85)*[83/2-(9/2)*sqrt(85)]^n, 
               with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Aug 28 2008]
%Y A099372 Sequence in context: A036354 A016948 A089683 this_sequence A036515 A046172 
               A123847
%Y A099372 Adjacent sequences: A099369 A099370 A099371 this_sequence A099373 A099374 
               A099375
%K A099372 nonn,easy
%O A099372 0,3
%A A099372 Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), 
               Oct 18 2004

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