Search: id:A056771
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%I A056771
%S A056771 1,17,577,19601,665857,22619537,768398401,26102926097,886731088897,
%T A056771 30122754096401,1023286908188737,34761632124320657,1180872205318713601,
%U A056771 40114893348711941777,1362725501650887306817,46292552162781456490001
%N A056771 a(n)=a(-n)=34a(n-1)-a(n-2) and a(0)=1.
%H A056771 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%H A056771 <a href="Sindx_Ch.html#Cheby">Index entries for sequences related to 
               Chebyshev polynomials.</a>
%F A056771 a(n) = (r^n+1/r^n)/2 with r = 17+sqrt(17^2-1) = 16*A001110(n)+1 = A001541(2n) 
               = (4*A001109(n))^2+1 = 3*A001109(2n-1)-A001109(2n-2) = A001109(2n)-3*A001109(2n-1).
%F A056771 a(n)= T(n, 17) = T(2*n, 3) with T(n, x) Chebyshev's polynomials of the 
               first kind. See A053120. T(n, 3)= A001541(n).
%F A056771 G.f.: (1-17*x)/(1-34*x+x^2).
%F A056771 a(n) = Cosh[2n*ArcSinh[Sqrt[8]]] - Herbert Kociemba (kociemba(AT)t-online.de), 
               Apr 24 2008
%o A056771 sage: [lucas_number2(n,34,1)/2 for n in xrange(0,15)] - Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Jun 27 2008
%Y A056771 Cf. A001075, A001541, A001091, A001079, A023038, A011943, A001081, A023039, 
               A001085 and note relationship with square triangular number sequences 
               A001110 and A001109.
%Y A056771 Sequence in context: A114063 A112716 A012069 this_sequence A041547 A041544 
               A009709
%Y A056771 Adjacent sequences: A056768 A056769 A056770 this_sequence A056772 A056773 
               A056774
%K A056771 nonn,easy
%O A056771 0,2
%A A056771 Henry Bottomley (se16(AT)btinternet.com), Aug 16 2000
%E A056771 More terms from James A. Sellers (sellersj(AT)math.psu.edu), Sep 07 2000
%E A056771 Chebyshev comments from W. Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), 
               Nov 29 2002

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