A257823 - OEIS

%I #10 Sep 08 2022 08:46:12

%S 413,531,8673,11269,426511,554187,9192849,11944727,452101247,

%T 587437689,9744411267,12661399351,479226895309,622683396153,

%U 10329066750171,13421071367333,507980056926293,660043812484491,10948801010769993,14226322987973629,538458381114975271

%N Positive integers whose square is the sum of 59 consecutive squares.

%C Positive integers x in the solutions to 2*x^2-118*y^2-6844*y-133458 = 0.

%H Colin Barker, <a href="/A257823/b257823.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1060,0,0,0,-1).

%F a(n) = 1060*a(n-4)-a(n-8).

%F G.f.: -59*x*(x-1)*(7*x^6+16*x^5+163*x^4+354*x^3+163*x^2+16*x+7) / (x^8-1060*x^4+1).

%e 413 is in the sequence because 413^2 = 170569 = 22^2+23^2+...+80^2.

%t LinearRecurrence[{0, 0, 0, 1060, 0, 0, 0, -1}, {413, 531, 8673, 11269, 426511, 554187, 9192849, 11944727}, 30] (* _Vincenzo Librandi_, May 11 2015 *)

%o (PARI) Vec(-59*x*(x-1)*(7*x^6+16*x^5+163*x^4+354*x^3+163*x^2+16*x+7) / (x^8-1060*x^4+1) + O(x^100))

%o (Magma) I:=[413,531,8673,11269,426511,554187,9192849, 11944727]; [n le 8 select I[n] else 1060*Self(n-4)-Self(n-8): n in [1..30]]; // _Vincenzo Librandi_, May 11 2015

%Y Cf. A001653, A180274, A218395, A257761, A257765, A257767, A257780, A257781, A257824-A257828.

%K nonn,easy

%O 1,1

%A _Colin Barker_, May 10 2015