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A207059
Nonnegative values x of solutions (x, y) to the Diophantine equation x^2 + (x+289)^2 = y^2.
10
119, 231, 300, 476, 867, 1496, 2120, 2511, 3519, 5780, 9435, 13067, 15344, 21216, 34391, 55692, 76860, 90131, 124355, 201144, 325295, 448671, 526020, 725492, 1173051, 1896656, 2615744, 3066567, 4229175, 6837740, 11055219, 15246371, 17873960, 24650136
OFFSET
1,1
COMMENTS
For the generic case x^2 + (x + p^2)^2 = y^2 with p = 2*m^2 - 1 a prime number in A066436, m>=3, (0; p^2) and (4*m^3 + 2*m^2 - 2*m - 1; 4*m^4 + 4*m^3 - 2*m - 1) are solutions. - Mohamed Bouhamida, Aug 24 2019
LINKS
Eric Weisstein, Diophantine equation (MathWorld).
FORMULA
G.f.: x*(85*x^9+48*x^8+23*x^7+48*x^6+85*x^5-391*x^4-176*x^3-69*x^2-112*x-119)/((x-1)*(x^10-6*x^5+1)). - Colin Barker, Aug 05 2012
a(n) = 6*a(n-5) - a(n-10) + 578 with a(1) = 119, a(2) = 231, a(3) = 300, a(4) = 476, a(5) = 867, a(6) = 1496, a(7) = 2120, a(8) = 2511, a(9) = 3519, a(10) = 5780. - Mohamed Bouhamida, Aug 24 2019
MATHEMATICA
LinearRecurrence[ {1, 0, 0, 0, 6, -6, 0, 0, 0, -1, 1}, {119, 231, 300, 476, 867, 1496, 2120, 2511, 3519, 5780, 9435}, 60]
PROG
(PARI) Vec(x*(85*x^9+48*x^8+23*x^7+48*x^6+85*x^5-391*x^4-176*x^3-69*x^2-112*x-119)/((x-1)*(x^10-6*x^5+1))+O(x^60)) \\ Stefano Spezia, Aug 24 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved