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A257823
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Positive integers whose square is the sum of 59 consecutive squares.
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11
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413, 531, 8673, 11269, 426511, 554187, 9192849, 11944727, 452101247, 587437689, 9744411267, 12661399351, 479226895309, 622683396153, 10329066750171, 13421071367333, 507980056926293, 660043812484491, 10948801010769993, 14226322987973629, 538458381114975271
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OFFSET
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1,1
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COMMENTS
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Positive integers x in the solutions to 2*x^2-118*y^2-6844*y-133458 = 0.
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LINKS
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FORMULA
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a(n) = 1060*a(n-4)-a(n-8).
G.f.: -59*x*(x-1)*(7*x^6+16*x^5+163*x^4+354*x^3+163*x^2+16*x+7) / (x^8-1060*x^4+1).
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EXAMPLE
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413 is in the sequence because 413^2 = 170569 = 22^2+23^2+...+80^2.
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MATHEMATICA
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LinearRecurrence[{0, 0, 0, 1060, 0, 0, 0, -1}, {413, 531, 8673, 11269, 426511, 554187, 9192849, 11944727}, 30] (* Vincenzo Librandi, May 11 2015 *)
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PROG
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(PARI) Vec(-59*x*(x-1)*(7*x^6+16*x^5+163*x^4+354*x^3+163*x^2+16*x+7) / (x^8-1060*x^4+1) + O(x^100))
(Magma) I:=[413, 531, 8673, 11269, 426511, 554187, 9192849, 11944727]; [n le 8 select I[n] else 1060*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, May 11 2015
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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