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A257781
Positive integers whose square is the sum of 50 consecutive squares.
12
245, 385, 495, 655, 795, 1055, 1365, 2205, 2855, 3795, 4615, 6135, 7945, 12845, 16635, 22115, 26895, 35755, 46305, 74865, 96955, 128895, 156755, 208395, 269885, 436345, 565095, 751255, 913635, 1214615, 1573005, 2543205, 3293615, 4378635, 5325055, 7079295
OFFSET
1,1
COMMENTS
Positive integers x in the solutions to 2*x^2-100*y^2-4900*y-80850 = 0.
FORMULA
a(n) = 6*a(n-6)-a(n-12).
G.f.: -5*x*(39*x^11 +31*x^10 +27*x^9 +23*x^8 +21*x^7 +21*x^6 -211*x^5 -159*x^4 -131*x^3 -99*x^2 -77*x -49) / ((x^6 -2*x^3 -1)*(x^6 +2*x^3 -1)).
EXAMPLE
245 is in the sequence because 245^2 = 60025 = 7^2+8^2+...+56^2.
MATHEMATICA
LinearRecurrence[{0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, -1}, {245, 385, 495, 655, 795, 1055, 1365, 2205, 2855, 3795, 4615, 6135}, 50] (* Vincenzo Librandi, May 11 2015 *)
PROG
(PARI) Vec(-5*x*(39*x^11 +31*x^10 +27*x^9 +23*x^8 +21*x^7 +21*x^6 -211*x^5 -159*x^4 -131*x^3 -99*x^2 -77*x -49) / ((x^6 -2*x^3 -1)*(x^6 +2*x^3 -1)) + O(x^100))
(Magma) I:=[245, 385, 495, 655, 795, 1055, 1365, 2205, 2855, 3795, 4615, 6135]; [n le 12 select I[n] else 6*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, May 11 2015
KEYWORD
nonn,easy
AUTHOR
Colin Barker, May 08 2015
STATUS
approved