%I #21 Sep 08 2022 08:46:12

%S 143,253,440,1133,1397,3608,6325,11495,20152,52063,64207,165880,

%T 290807,528517,926552,2393765,2952125,7626872,13370797,24300287,

%U 42601240,110061127,135733543,350670232,614765855,1117284685,1958730488,5060418077,6240790853

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

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

%H Colin Barker, <a href="/A257767/b257767.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,46,0,0,0,0,0,-1).

%F a(n) = 46*a(n-6)-a(n-12).

%F 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).

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

%t 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 *)

%o (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))

%o (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

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

%K nonn,easy

%O 1,1

%A _Colin Barker_, May 07 2015