A257767 Positive integers whose square is the sum of 33 consecutive squares.

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.

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,46,0,0,0,0,0,-1).

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

Crossrefs

Cf. A001032, A001653, A180274, A218395, A257761, A257765, A257780, A257781, A257823-A257828.

Sequence in context: A227868 A353059 A176876 * A158136 A153874 A003902

Adjacent sequences: A257764 A257765 A257766 * A257768 A257769 A257770

Keyword

nonn,easy

Author

Colin Barker, May 07 2015

Status

approved