Search: id:A118675
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%I A118675
%S A118675 0,16,85,141,225,616,940,1428,3705,5593,8437,21708,32712,49288,126637,
%T A118675 190773,287385,738208,1112020,1675116,4302705,6481441,9763405,25078116,
%U A118675 37776720,56905408,146166085,220178973,331669137,851918488,1283297212
%N A118675 Nonnegative values x of solutions (x, y) to the Diophantine equation 
               x^2+(x+47)^2 = y^2.
%C A118675 Also values x of Pythagorean triples (x, x+47, y).
%C A118675 Corresponding values y of solutions (x, y) are in A159750.
%C A118675 For the generic case x^2+(x+p)^2 = y^2 with p = m^2-2 a (prime) number 
               > 7 in A028871, see A118337.
%C A118675 lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).
%C A118675 lim_{n -> infinity} a(n)/a(n-1) = (51+14*sqrt(2))/47 for n mod 3 = {1, 
               2}.
%C A118675 lim_{n -> infinity} a(n)/a(n-1) = (3267+1702*sqrt(2))/47^2 for n mod 
               3 = 0.
%F A118675 a(n) = 6*a(n-3)-a(n-6)+94 for n > 6; a(1)=0, a(2)=16, a(3)=85, a(4)=141, 
               a(5)=225, a(6)=616.
%F A118675 G.f.: x*(16+69*x+56*x^2-12*x^3-23*x^4-12*x^5)/((1-x)*(1-6*x^3+x^6)).
%F A118675 a(3*k+1) = 47*A001652(k) for k >= 0.
%o A118675 (PARI) {forstep(n=0, 100000000, [1, 3], if(issquare(2*n^2+94+2209), print1(n, 
               ",")))}
%Y A118675 Cf. A159750, A028871, A118337, A001652, A156035 (decimal expansion of 
               3+2*sqrt(2)), A159751 (decimal expansion of (51+14*sqrt(2))/47), 
               A159752 (decimal expansion of (3267+1702*sqrt(2))/47^2).
%Y A118675 Sequence in context: A151502 A030693 A159501 this_sequence A070052 A022676 
               A035291
%Y A118675 Adjacent sequences: A118672 A118673 A118674 this_sequence A118676 A118677 
               A118678
%K A118675 nonn
%O A118675 1,2
%A A118675 Mohamed Bouhamida (bhmd95(AT)yahoo.fr), May 19 2006
%E A118675 Edited by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Apr 30 2009

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