cp's OEIS Frontend

A161487 Positive numbers y such that y^2 is of the form x^2+(x+191)^2 with integer x.

%I A161487 #2 Mar 30 2012 17:28:02
%S A161487 149,191,269,625,955,1465,3601,5539,8521,20981,32279,49661,122285,
%T A161487 188135,289445,712729,1096531,1687009,4154089,6391051,9832609,
%U A161487 24211805,37249775,57308645,141116741,217107599,334019261,822488641,1265395819
%N A161487 Positive numbers y such that y^2 is of the form x^2+(x+191)^2 with integer x.
%C A161487 (-51, a(1)) and (A161486(n), a(n+1)) are solutions (x, y) to the Diophantine equation x^2+(x+191)^2 = y^2.
%C A161487 lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).
%C A161487 lim_{n -> infinity} a(n)/a(n-1) = (209+60*sqrt(2))/191 for n mod 3 = {0, 2}.
%C A161487 lim_{n -> infinity} a(n)/a(n-1) = (52323+26522*sqrt(2))/191^2 for n mod 3 = 1.
%F A161487 a(n) = 6*a(n-3)-a(n-6) for n > 6; a(1)=149, a(2)=191, a(3)=269, a(4)=625, a(5)=955, a(6)=1465.
%F A161487 G.f.: (1-x)*(149+340*x+609*x^2+340*x^3+149*x^4) / (1-6*x^3+x^6).
%F A161487 a(3*k-1) = 191*A001653(k) for k >= 1.
%e A161487 (-51, a(1)) = (-51, 149) is a solution: (-51)^2+(-51+191)^2 = 2601+19600 = 22201 = 149^2.
%e A161487 (A161486(1), a(2)) = (0, 191) is a solution: 0^2+(0+191)^2 = 36481 = 191^2.
%e A161487 (A161486(3), a(4)) = (336, 625) is a solution: 336^2+(336+191)^2 = 112896+277729 = 390625 = 625^2.
%o A161487 (PARI) {forstep(n=-52, 100000000, [1, 3], if(issquare(2*n^2+382*n+36481, &k), print1(k, ",")))}
%Y A161487 Cf. A161486, A001653, A156035 (decimal expansion of 3+2*sqrt(2)), A161488 (decimal expansion of (209+60*sqrt(2))/191), A161489 (decimal expansion of (52323+26522*sqrt(2))/191^2).
%K A161487 nonn
%O A161487 1,1
%A A161487 _Klaus Brockhaus_, Jun 13 2009