Search: id:A038762
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%I A038762
%S A038762 3,13,75,437,2547,14845,86523,504293,2939235,17131117,99847467,
%T A038762 581953685,3391874643,19769294173,115223890395,671574048197,
%U A038762 3914220398787,22813748344525,132968269668363,774995869665653
%N A038762 a(n)=6a(n-1)-a(n-2) for n >= 2, with a(0)=3, a(1)=13.
%C A038762 A Pellian-related sequence.
%C A038762 a(n)={13*([3+2*sqrt(2)]^n -[3-2*sqrt(2)]^n)-3*([3+2*sqrt(2)]^(n-1) - 
               [3-2*sqrt(2)]^(n-1))}/(4*sqrt(2)).
%D A038762 A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, 
               pp. 122-125, 194-196.
%D A038762 M. J. DeLeon, Pell's Equation and Pell Number Triples, Fib. Quart., 14(1976), 
               pp. 456-460.
%H A038762 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A038762 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%F A038762 Equals sqrt{2*(A038761)^2+7}.
%F A038762 a(n) = 7*a(n-1) - 7*a(n-2) + a(n-3); a(n) = (1/2)*(3+sqrt(2))*(3+2*sqrt(2))^(n-1)+(1/
               2)*(3-sqrt(2))*(3-2*sqrt(2))^(n-1). - Antonio A. Olivares (olivares14031(AT)yahoo.com), 
               Apr 20 2008
%F A038762 G.f.: (3-x)/(1-6*x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Nov 03 2008]
%Y A038762 Cf. A038761.
%Y A038762 a(n) = A077443(2n) = A038725(n)+A038725(n+1).
%Y A038762 Sequence in context: A020094 A009382 A110193 this_sequence A074517 A007178 
               A034172
%Y A038762 Adjacent sequences: A038759 A038760 A038761 this_sequence A038763 A038764 
               A038765
%K A038762 easy,nonn
%O A038762 0,1
%A A038762 Barry E. Williams, May 03 2000
%E A038762 More terms from James A. Sellers (sellersj(AT)math.psu.edu), May 04 2000

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