

A129641


Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+409)^2 = y^2.


5



0, 200, 611, 1227, 2291, 4620, 8180, 14364, 27927, 48671, 84711, 163760, 284664, 494720, 955451, 1660131, 2884427, 5569764, 9676940, 16812660, 32463951, 56402327, 97992351, 189214760, 328737840, 571142264, 1102825427, 1916025531, 3328862051, 6427738620
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OFFSET

1,2


COMMENTS

Also values x of Pythagorean triples (x, x+409, y).
Corresponding values y of solutions (x, y) are in A160577.
lim_{n > infinity} a(n)/a(n3) = 3+2*sqrt(2).
lim_{n > infinity} a(n)/a(n1) = (473+168*sqrt(2))/409 for n mod 3 = {1, 2}.
lim_{n > infinity} a(n)/a(n1) = (204819+83570*sqrt(2))/409^2 for n mod 3 = 0.


LINKS

Table of n, a(n) for n=1..30.
Index entries for linear recurrences with constant coefficients, signature (1,0,6,6,0,1,1).


FORMULA

a(n) = 6*a(n3)a(n6)+818 for n > 6; a(1)=0, a(2)=200, a(3)=611, a(4)=1227, a(5)=2291, a(6)=4620.
G.f.: x*(200+411*x+616*x^2136*x^3137*x^4136*x^5)/((1x)*(16*x^3+x^6)).
a(3*k+1) = 409*A001652(k) for k >= 0.


MATHEMATICA

LinearRecurrence[{1, 0, 6, 6, 0, 1, 1}, {0, 200, 611, 1227, 2291, 4620, 8180}, 50] (* Vladimir Joseph Stephan Orlovsky, Feb 13 2012 *)


PROG

(PARI) {forstep(n=0, 10000000, [3, 1], if(issquare(2*n^2+818*n+167281), print1(n, ", ")))}


CROSSREFS

Cf. A160577, A001652, A129640, A156035 (decimal expansion of 3+2*sqrt(2)), A160578 (decimal expansion of (473+168*sqrt(2))/409), A160579 (decimal expansion of (204819+83570*sqrt(2))/409^2).
Sequence in context: A109632 A258921 A258918 * A202966 A218846 A219425
Adjacent sequences: A129638 A129639 A129640 * A129642 A129643 A129644


KEYWORD

nonn,easy


AUTHOR

Mohamed Bouhamida (bhmd95(AT)yahoo.fr), May 31 2007


EXTENSIONS

Edited and two terms added by Klaus Brockhaus, Jun 08 2009


STATUS

approved



