|
Search: id:A129288
|
|
|
| A129288 |
|
Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+41)^2 = y^2. |
|
+0
11
|
|
| 0, 36, 39, 123, 319, 336, 820, 1960, 2059, 4879, 11523, 12100, 28536, 67260, 70623, 166419, 392119, 411720, 970060, 2285536, 2399779, 5654023, 13321179, 13987036, 32954160, 77641620, 81522519, 192071019, 452528623, 475148160, 1119472036
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
Also values x of Pythagorean triples (x, x+41, y).
Corresponding values y of solutions (x, y) are in A157257.
lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).
lim_{n -> infinity} a(n)/a(n-1) = (7+2*sqrt(2))/(7-2*sqrt(2)) for n mod 3 = {1, 2}.
lim_{n -> infinity} a(n)/a(n-1) = (3+2*sqrt(2))*(7-2*sqrt(2))^2/(7+2*sqrt(2))^2 for n mod 3 = 0.
|
|
FORMULA
|
a(n) = 6*a(n-3)-a(n-6)+82 for n > 6; a(1)=0, a(2)=36, a(3)=39, a(4)=123, a(5)=319, a(6)=336.
G.f.: x*(36+3*x+84*x^2-20*x^3-x^4-20*x^5)/((1-x)*(1-6*x^3+x^6))
a(3*k+1) = 41*A001652(k) for k >= 0.
|
|
PROGRAM
|
(PARI) {forstep(n=0, 1200000000, [3 , 1], if(issquare(2*n^2+82*n+1681), print1(n, ", ")))}
|
|
CROSSREFS
|
Cf. A157257, A001652, A156035 (decimal expansion of 3+2*sqrt(2)), A157258 (decimal expansion of 7+2*sqrt(2)), A157259 (decimal expansion of 7-2*sqrt(2)), A157260 (decimal expansion of (7+2*sqrt(2))/(7-2*sqrt(2))).
Sequence in context: A165857 A098079 A031317 this_sequence A083248 A077090 A067672
Adjacent sequences: A129285 A129286 A129287 this_sequence A129289 A129290 A129291
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Mohamed Bouhamida (bhmd95(AT)yahoo.fr), May 26 2007
|
|
EXTENSIONS
|
Edited and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Feb 26 2009
|
|
|
Search completed in 0.002 seconds
|
