Search: id:A054492
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%I A054492
%S A054492 1,6,17,45,118,309,809,2118,5545,14517,38006,99501,260497,681990,
%T A054492 1785473,4674429,12237814,32039013,83879225,219598662,574916761,
%U A054492 1505151621,3940538102,10316462685,27008849953,70710087174
%N A054492 a(n)=3a(n-1)-a(n-2), a(0)=1,a(0)=6.
%D A054492 I. Adler, Three Diophantine equations - Part II, Fib. Quart., 7 (1969), 
               pps. 181-193.
%D A054492 A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, 
               pps. 122-125, 194-196.
%D A054492 E. I. Emerson, Recurrent Sequences in the Equation DQ^2=R^2+N, Fib. Quart., 
               7 (1969), pps. 231-242.
%H A054492 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A054492 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%F A054492 2*Lucas(2n+1) - Fibonacci(2n+1).
%F A054492 G.f.: (1+3*x)/(1-3*x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Nov 03 2008]
%e A054492 a(n)={6*([(3+sqrt(5))/2]^n-[(3-sqrt(5))/2]^n)-([(3+sqrt(5))/2]^(n-1)-[(3-sqrt(5))/
               2]^(n-1))}/sqrt(5).
%Y A054492 Cf. A002878 and A054486.
%Y A054492 Sequence in context: A066183 A048746 A026382 this_sequence A128525 A083334 
               A088016
%Y A054492 Adjacent sequences: A054489 A054490 A054491 this_sequence A054493 A054494 
               A054495
%K A054492 easy,nonn
%O A054492 0,2
%A A054492 Barry E. Williams, May 06 2000

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