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A207059
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Nonnegative values x of solutions (x, y) to the Diophantine equation x^2 + (x+289)^2 = y^2.
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8
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Eric Weisstein, Diophantine equation (MathWorld).
Wikipedia, Diophantine equation
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,6,-6,0,0,0,-1,1).
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FORMULA
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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
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MATHEMATICA
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LinearRecurrence[ {1, 0, 0, 0, 6, -6, 0, 0, 0, -1, 1}, {119, 231, 300, 476, 867, 1496, 2120, 2511, 3519, 5780, 9435}, 60]
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PROG
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(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
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CROSSREFS
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Cf. A204765, A205644, A205672, A207058.
Sequence in context: A134604 A255580 A227515 * A257603 A063348 A243581
Adjacent sequences: A207056 A207057 A207058 * A207060 A207061 A207062
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KEYWORD
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nonn,easy
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AUTHOR
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Vladimir Joseph Stephan Orlovsky, Feb 14 2012
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STATUS
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approved
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