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

Author

Colin Barker, May 07 2015

Keywords

• nonn
• easy

Comments

Positive integers x in the solutions to 2*x^2-66*y^2-2112*y-22880 = 0.

Examples

			143 is in the sequence because 143^2 = 20449 = 7^2+8^2+...+39^2.
		

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).

Crossrefs

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

Programs

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

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 *)

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))

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).