|
| |
|
|
A129625
|
|
Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+233)^2 = y^2.
|
|
4
| |
|
|
0, 75, 432, 699, 1092, 3115, 4660, 6943, 18724, 27727, 41032, 109695, 162168, 239715, 639912, 945747, 1397724, 3730243, 5512780, 8147095, 21742012, 32131399, 47485312, 126722295, 187276080, 276765243, 738592224, 1091525547, 1613106612
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| Also values x of Pythagorean triples (x, x+233, y).
Corresponding values y of solutions (x, y) are in A157297.
lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).
lim_{n -> infinity} a(n)/a(n-1) = (251+66*sqrt(2))/233 for n mod 3 = {1, 2}.
lim_{n -> infinity} a(n)/a(n-1) = (82611+44030*sqrt(2))/233^2 for n mod 3 = 0.
|
|
|
LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (1,0,6,-6,0,-1,1).
|
|
|
FORMULA
| a(n) = 6*a(n-3)-a(n-6)+466 for n > 6; a(1)=0, a(2)=75, a(3)=432, a(4)=699, a(5)=1092, a(6)=3115.
G.f.: x*(75+357*x+267*x^2-57*x^3-119*x^4-57*x^5)/((1-x)*(1-6*x^3+x^6)).
a(3*k+1) = 233*A001652(k) for k >= 0.
|
|
|
PROG
| (PARI) {forstep(n=0, 1700000000, [3, 1], if(issquare(2*n^2+466*n+54289), print1(n, ", ")))}
|
|
|
CROSSREFS
| Cf. A157297, A001652, A129288, A129289, A129298, A156035 (decimal expansion of 3+2*sqrt(2)), A157298 (decimal expansion of (251+66*sqrt(2))/233), A157299 (decimal expansion of (82611+44030*sqrt(2))/233^2).
Sequence in context: A055561 A193252 A015223 * A133382 A199901 A202257
Adjacent sequences: A129622 A129623 A129624 * A129626 A129627 A129628
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| Mohamed Bouhamida (bhmd95(AT)yahoo.fr), May 30 2007
|
|
|
EXTENSIONS
| Edited and two terms added by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Apr 11 2009
|
| |
|
|
