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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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Positive integers x in the solutions to 2*x^2-100*y^2-4900*y-80850 = 0.
LINKS
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
CROSSREFS
Sequence in context: A171994 A129210 A137521 * A188239 A132830 A350421
KEYWORD
nonn,easy
AUTHOR
Colin Barker, May 08 2015
STATUS
approved

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Last modified March 29 02:15 EDT 2024. Contains 371264 sequences. (Running on oeis4.)