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A257767
Positive integers whose square is the sum of 33 consecutive squares.
12
143, 253, 440, 1133, 1397, 3608, 6325, 11495, 20152, 52063, 64207, 165880, 290807, 528517, 926552, 2393765, 2952125, 7626872, 13370797, 24300287, 42601240, 110061127, 135733543, 350670232, 614765855, 1117284685, 1958730488, 5060418077, 6240790853
OFFSET
1,1
COMMENTS
Positive integers x in the solutions to 2*x^2-66*y^2-2112*y-22880 = 0.
FORMULA
a(n) = 46*a(n-6)-a(n-12).
G.f.: -11*x*(8*x^11+5*x^10+5*x^9+8*x^8+13*x^7+23*x^6-328*x^5-127*x^4-103*x^3-40*x^2-23*x-13) / (x^12-46*x^6+1).
EXAMPLE
143 is in the sequence because 143^2 = 20449 = 7^2+8^2+...+39^2.
MATHEMATICA
LinearRecurrence[{0, 0, 0, 0, 0, 46, 0, 0, 0, 0, 0, -1}, {143, 253, 440, 1133, 1397, 3608, 6325, 11495, 20152, 52063, 64207, 165880}, 50] (* Vincenzo Librandi, May 08 2015 *)
PROG
(PARI) Vec(-11*x*(8*x^11+5*x^10+5*x^9+8*x^8+13*x^7+23*x^6-328*x^5-127*x^4-103*x^3-40*x^2-23*x-13) / (x^12-46*x^6+1) + O(x^100))
(Magma) I:=[143, 253, 440, 1133, 1397, 3608, 6325, 11495, 20152, 52063, 64207, 165880]; [n le 12 select I[n] else 46*Self(n-6)-Self(n-12): n in [1..30]]; // Vincenzo Librandi, May 11 2015
KEYWORD
nonn,easy
AUTHOR
Colin Barker, May 07 2015
STATUS
approved