Search: id:A099374
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%I A099374
%S A099374 0,1,100,10201,1040400,106110601,10822240900,1103762461201,
%T A099374 112572948801600,11481337015302001,1170983802612002500,
%U A099374 119428866529408953001,12180573402197101203600
%N A099374 Squares of A041041(n-1), n>=1 (generalized Fibonacci).
%C A099374 See the comment in A099279. This is example a=10.
%H A099374 <a href="Sindx_Ch.html#Cheby">Index entries for sequences related to 
               Chebyshev polynomials.</a>
%F A099374 a(n)= A041041(n-1)^2, n>=1, a(0)=0.
%F A099374 a(n)= 101*a(n-1) + 101*a(n-2) - a(n-3), n>=3; a(0)=0, a(1)=1, a(2)=100.
%F A099374 a(n)= 102*a(n-1) - a(n-2) - 2*(-1)^n, n>=2; a(0)=0, a(1)=1.
%F A099374 a(n)= (T(n, 51)-(-1)^n)/52 with the Chebyshev's polynomials of the first 
               kind: T(n, 51)=(n).
%F A099374 G.f.: x*(1-x)/((1-102*x+x^2)*(1+x)) = x*(1-x)/(1-101*x-101*x^2+x^3).
%F A099374 a(n)=-(1/52)*(-1)^n+(1/104)*[51+10*sqrt(26)]^n+(1/104)*[51-10*sqrt(26)]^n, 
               with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Aug 28 2008]
%Y A099374 Sequence in context: A045799 A096885 A027576 this_sequence A163663 A151648 
               A013747
%Y A099374 Adjacent sequences: A099371 A099372 A099373 this_sequence A099375 A099376 
               A099377
%K A099374 nonn,easy
%O A099374 0,3
%A A099374 Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), 
               Oct 18 2004

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