Search: id:A038725
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%I A038725
%S A038725 1,2,11,64,373,2174,12671,73852,430441,2508794,14622323,85225144,
%T A038725 496728541,2895146102,16874148071,98349742324,573224305873,
%U A038725 3340996092914,19472752251611,113495517416752,661500352248901
%N A038725 a(n)=6a(n-1)-a(n-2), n >= 2, a(0)=1, a(1)=2.
%D A038725 I. Adler, Three Diophantine equations - Part II, Fib. Quart.,7 (1969), 
               pps. 181-193.
%D A038725 A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, 
               pps. 122-125, 194-196.
%D A038725 E. I. Emerson, Recurrent Sequences in the Equation DQ^2=R^2+N, Fib. Quart., 
               7(1969), pps. 231-242.
%H A038725 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A038725 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%F A038725 a(n) = 7*a(n-1) - 7*a(n-2) + a(n-3); a(n) = ((4-sqrt(2))/8)*(3+2*sqrt(2))^(n-1)+((4+sqrt(2))/
               8)*(3-2*sqrt(2))^(n-1). - Antonio A. Olivares (olivares14031(AT)yahoo.com), 
               Mar 29 2008
%F A038725 Sequence satisfies -7 = f(a(n), a(n+1)) where f(u, v) = u^2 + v^2 - 6*u*v. 
               - Michael Somos Sep 28 2008
%F A038725 G.f.: (1 - 4*x) / (1 - 6*x + x^2). a(n) = (7 + a(n-1)^2) / a(n-2). - 
               Michael Somos Sep 28 2008
%p A038725 a[0]:=1: a[1]:=2: for n from 2 to 26 do a[n]:=6*a[n-1]-a[n-2] od: seq(a[n], 
               n=0..20); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 26 
               2006
%o A038725 (PARI) {a(n) = real((3 + 2*quadgen(8))^n * (1 - quadgen(8) / 4))} /* 
               Michael Somos Sep 28 2008 */
%o A038725 (PARI) {a(n) = polchebyshev(n, 1, 3) - polchebyshev(n-1, 2, 3)} /* Michael 
               Somos Sep 28 2008 */
%Y A038725 Cf. A001653 and A001541.
%Y A038725 A038723(n) = a(-n).
%Y A038725 Sequence in context: A114175 A080049 A126745 this_sequence A161947 A001565 
               A074613
%Y A038725 Adjacent sequences: A038722 A038723 A038724 this_sequence A038726 A038727 
               A038728
%K A038725 easy,nonn
%O A038725 0,2
%A A038725 Barry E. Williams, May 02 2000
%E A038725 More terms from James A. Sellers (sellersj(AT)math.psu.edu), May 03 2000

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