Search: id:A038723
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%I A038723
%S A038723 1,4,23,134,781,4552,26531,154634,901273,5253004,30616751,178447502,
%T A038723 1040068261,6061962064,35331704123,205928262674,1200237871921,
%U A038723 6995498968852,40772755941191,237641036678294,1385073464128573
%N A038723 a(n)=6a(n-1)-a(n-2), n >= 2, a(0)=1, a(1)=4.
%D A038723 I. Adler, Three Diophantine equations - Part II, Fib. Quart., 7(1969), 
               pps. 181-193.
%D A038723 A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, 
               pps. 122-125, 194-196.
%D A038723 E. I. Emerson, Recurrent Sequences in the Equation DQ^2=R^2+N, Fib. Quart., 
               7(1969), pps. 231-242.
%H A038723 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A038723 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%F A038723 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 A038723 a(n) = a001653(n) - a001653(n - 1) - ... - a001653(n - (n - 1)) - Antonio 
               A. Olivares (olivares14031(AT)yahoo.com), Mar 29 2008
%F A038723 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 A038723 G.f.: (1 - 2*x) / (1 - 6*x + x^2). a(n) = (7 + a(n-1)^2) / a(n-2). - 
               Michael Somos Sep 28 2008
%p A038723 a[0]:=1: a[1]:=4: 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 A038723 (PARI) {a(n) = real((3 + 2*quadgen(8))^n * (1 + quadgen(8) / 4))} /* 
               Michael Somos Sep 28 2008 */
%o A038723 (PARI) {a(n) = polchebyshev(n, 1, 3) + polchebyshev(n-1, 2, 3)} /* Michael 
               Somos Sep 28 2008 */
%Y A038723 Cf. A001653, A001541, A038725.
%Y A038723 Cf. A001653.
%Y A038723 A038725(n) = a(-n).
%Y A038723 Sequence in context: A015532 A144465 A024050 this_sequence A091640 A067110 
               A158197
%Y A038723 Adjacent sequences: A038720 A038721 A038722 this_sequence A038724 A038725 
               A038726
%K A038723 easy,nonn
%O A038723 0,2
%A A038723 Barry E. Williams, May 02 2000
%E A038723 More terms from James A. Sellers (sellersj(AT)math.psu.edu), May 03 2000

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