Search: id:A098301
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%I A098301
%S A098301 0,1,16,225,3136,43681,608400,8473921,118026496,1643897025,22896531856,
%T A098301 318907548961,4441809153600,61866420601441,861688079266576,
%U A098301 12001766689130625,167163045568562176,2328280871270739841
%N A098301 Member r=16 of the family of Chebyshev sequences S_r(n) defined in A092184.
%H A098301 <a href="Sindx_Ch.html#Cheby">Index entries for sequences related to 
               Chebyshev polynomials.</a>
%F A098301 a(n)= (T(n, 7)-1)/6 with Chebyshev's polynomials of the first kind evaluated 
               at x=7: T(n, 7)=A011943(n)=((7+4*sqrt(3))^n + (7-4*sqrt(3))^n)/2.
%F A098301 a(n)= A001353(n)^2 = S(n-1, 4)^2 with Chebyshev's polynomials of the 
               second kind evaluated at x=4, S(n, 4):=U(n, 2).
%F A098301 a(n)= 14*a(n-1) - a(n-2) + 2, n>=2, a(0)=0, a(1)=1.
%F A098301 a(n)= 15*a(n-1) - 15*a(n-2) + a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=16.
%F A098301 G.f.: x*(1+x)/((1-x)*(1-14*x+x^2)) = x*(1+x)/(1-15*x+15*x^2-x^3) (from 
               the Stephan link, see A092184).
%F A098301 4*A007655(n+1) + A046184(n) = A055793(n+2) + a(n+1) (conjecture) - Creighton 
               Dement (creighton.k.dement(AT)uni-oldenburg.de), Nov 01 2004
%Y A098301 Sequence in context: A118779 A051822 A017438 this_sequence A014897 A048445 
               A028340
%Y A098301 Adjacent sequences: A098298 A098299 A098300 this_sequence A098302 A098303 
               A098304
%K A098301 nonn,easy
%O A098301 0,3
%A A098301 Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), 
               Oct 18 2004

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