|
| |
|
|
A129975
|
|
Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+953)^2 = y^2.
|
|
4
| |
|
|
0, 132, 2295, 2859, 3535, 15792, 19060, 22984, 94363, 113407, 136275, 552292, 663288, 796572, 3221295, 3868227, 4645063, 18777384, 22547980, 27075712, 109444915, 131421559, 157811115, 637894012, 765983280, 919792884, 3717921063
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| Also values x of Pythagorean triples (x, x+953, y).
Corresponding values y of solutions (x, y) are in A160212.
lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).
lim_{n -> infinity} a(n)/a(n-1) = (969+124*sqrt(2))/953 for n mod 3 = {1, 2}.
lim_{n -> infinity} a(n)/a(n-1) = (1947891+1218490*sqrt(2))/953^2 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)+1906 for n > 6; a(1)=0, a(2)=132, a(3)=2295, a(4)=2859, a(5)=3535, a(6)=15792.
G.f.: x*(132+2163*x+564*x^2-116*x^3-721*x^4-116*x^5) / ((1-x)*(1-6*x^3+x^6)).
a(3*k+1) = 953*A001652(k) for k >= 0.
|
|
|
PROG
| (PARI) {forstep(n=0, 10000000, [3, 1], if(issquare(2*n^2+1906*n+908209), print1(n, ", ")))}
|
|
|
CROSSREFS
| Cf. A160212, A001652, A129974, A156035 (decimal expansion of 3+2*sqrt(2)), A160213 (decimal expansion of (969+124*sqrt(2))/953), A160214 (decimal expansion of (1947891+1218490*sqrt(2))/953^2).
Sequence in context: A090199 A033278 A119982 * A064303 A023902 A168180
Adjacent sequences: A129972 A129973 A129974 * A129976 A129977 A129978
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Jun 13 2007
|
|
|
EXTENSIONS
| Edited and two terms added by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 18 2009
|
| |
|
|
