%I A077445
%S A077445 4,20,116,676,3940,22964,133844,780100,4546756,26500436,154455860,
%T A077445 900234724,5246952484,30581480180,178241928596,1038870091396,
%U A077445 6054978619780,35291001627284,205691031143924,1198855185236260
%N A077445 Numbers n such that (n^2 - 8)/2 is a square.
%C A077445 The equation "(n^2 - 8)/2 is a square" is a version of the generalized 
               Pell Equation "x^2 - D*y^2 = C".
%D A077445 A. H. Beiler, "The Pellian." Ch. 22 in Recreations in the Theory of Numbers: 
               The Queen of Mathematics Entertains. Dover, New York, New York, pp. 
               248-268, 1966.
%D A077445 L. E. Dickson, History of the Theory of Numbers, Vol. II, Diophantine 
               Analysis. AMS Chelsea Publishing, Providence, Rhode Island, 1999, 
               p. 341-400.
%D A077445 Peter G. L. Dirichlet, Lectures on Number Theory (History of Mathematics 
               Source Series, V. 16); American Mathematical Society, Providence, 
               Rhode Island, 1999, p. 139-147.
%H A077445 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A077445 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%H A077445 J. J. O'Connor and E. F. Robertson, <a href="http://www-gap.dcs.st-and.ac.uk/
               ~history/HistTopics/Pell.html">Pell's Equation</a>
%H A077445 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PellEquation.html">; Pell Equation</a>
%F A077445 a(n) =[ [(3+2*Sqrt(2))^n + (3-2*Sqrt(2))^n] + [(3+2*Sqrt(2))^(n-1) + 
               (3-2*Sqrt(2))^(n-1)] ] / 2. a(n) = 6*a(n-1) - a(n-2)
%F A077445 G.f.: 4(x-x^2)/(1-6x+x^2).
%F A077445 With a=3+2sqrt(2), b=3-2sqrt(2): a(n)=sqrt(2)(a^((2n-1)/2)+b^((2n-1)/
               2)). a(n)=sqrt(2*A003499(2n-1)+4). - Mario Catalani (mario.catalani(AT)unito.it), 
               Mar 24 2003
%F A077445 a(n)=(A003499(n+1)+A003499(n))/2 - Mario Catalani (mario.catalani(AT)unito.it), 
               Mar 31 2003
%F A077445 a(n) = 7*a(n-1) - 7*a(n-2) + a(n-3); a(0) = 4, a(1) = 20, a(2) = 116; 
               a(n) = (2 + SQRT(2))*(3 + 2*SQRT(2))^n + (2 - SQRT(2))*(3- 2*SQRT(2))^n 
               - Antonio A. Olivares (olivares14031(AT)gmail.com), Feb 23 2006
%o A077445 (PARI) a(n)=if(n<1,0,subst(poltchebi(n)+poltchebi(n-1),x,3))
%Y A077445 (a(n))^2 - 2*(A077444(n)) = 8.
%Y A077445 Sequence in context: A128327 A100034 A106567 this_sequence A085458 A085456 
               A120915
%Y A077445 Adjacent sequences: A077442 A077443 A077444 this_sequence A077446 A077447 
               A077448
%K A077445 nonn
%O A077445 1,1
%A A077445 Gregory V. Richardson (omomom(AT)hotmail.com), Nov 09 2002