Search: id:A077412
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%I A077412
%S A077412 1,16,255,4064,64769,1032240,16451071,262184896,4178507265,66593931344,
%T A077412 1061324394239,16914596376480,269572217629441,4296240885694576,
%U A077412 68470281953483775,1091228270370045824,17391182043967249409
%N A077412 Chebyshev U(n,x) polynomial evaluated at x=8.
%H A077412 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A077412 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%H A077412 <a href="Sindx_Ch.html#Cheby">Index entries for sequences related to 
               Chebyshev polynomials.</a>
%F A077412 a(n) = 16*a(n-1) - a(n-2), n>=1, a(-1)=0, a(0)=1.
%F A077412 a(n) = S(n, 16) with S(n, x) := U(n, x/2), Chebyshev's polynomials of 
               the second kind. See A049310.
%F A077412 G.f.: 1/(1-16*x+x^2).
%F A077412 a(n) = (((8+3*sqrt(7))^(n+1) - (8-3*sqrt(7))^(n+1)))/(6*sqrt(7)).
%F A077412 a(n) = sqrt(A001081(n+1)^2-1)/63).
%F A077412 a(n+1)=16a(n)- a(n-1) a(1)=1 , a(2)=16 [From Sture Sjoestedt (sture.sjostedt(AT)spray.se), 
               May 31 2009]
%F A077412 a(n)=((8+Sqrt(63))^n -(8-Sqrt(63)^n)/(2*Sqrt(63)) [From Sture Sjoestedt 
               (sture.sjostedt(AT)spray.se), May 31 2009]
%t A077412 lst={};Do[AppendTo[lst, GegenbauerC[n, 1, 8]], {n, 0, 8^2}];lst [From 
               Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 11 2008]
%o A077412 sage: [lucas_number1(n,16,1) for n in xrange(1,20)] - Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Jun 25 2008
%Y A077412 Sequence in context: A138460 A110394 A158531 this_sequence A135554 A017570 
               A016744
%Y A077412 Adjacent sequences: A077409 A077410 A077411 this_sequence A077413 A077414 
               A077415
%K A077412 nonn,easy
%O A077412 0,2
%A A077412 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Nov 08 
               2002

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