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A257823
Positive integers whose square is the sum of 59 consecutive squares.
11
413, 531, 8673, 11269, 426511, 554187, 9192849, 11944727, 452101247, 587437689, 9744411267, 12661399351, 479226895309, 622683396153, 10329066750171, 13421071367333, 507980056926293, 660043812484491, 10948801010769993, 14226322987973629, 538458381114975271
OFFSET
1,1
COMMENTS
Positive integers x in the solutions to 2*x^2-118*y^2-6844*y-133458 = 0.
FORMULA
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).
EXAMPLE
413 is in the sequence because 413^2 = 170569 = 22^2+23^2+...+80^2.
MATHEMATICA
LinearRecurrence[{0, 0, 0, 1060, 0, 0, 0, -1}, {413, 531, 8673, 11269, 426511, 554187, 9192849, 11944727}, 30] (* Vincenzo Librandi, May 11 2015 *)
PROG
(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
KEYWORD
nonn,easy
AUTHOR
Colin Barker, May 10 2015
STATUS
approved