A262018 - OEIS

%I #7 May 16 2019 11:31:45

%S 28,5308,945148,168231388,29944242268,5329906892668,948693482652988,

%T 168862110005339548,30056506887467786908,5349889363859260730428,

%U 952250250260060942229628,169495194656926988456143708,30169192398682743884251350748,5369946751770871484408284289788

%N The first of five consecutive positive integers the sum of the squares of which is equal to the sum of the squares of eleven consecutive positive integers.

%C For the first of the corresponding eleven consecutive positive integers, see A262019.

%H Colin Barker, <a href="/A262018/b262018.txt">Table of n, a(n) for n = 1..444</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (179,-179,1).

%F a(n) = 179*a(n-1)-179*a(n-2)+a(n-3) for n>3.

%F G.f.: -4*x*(7*x^2+74*x+7) / ((x-1)*(x^2-178*x+1)).

%e 28 is in the sequence because 28^2 + ... + 32^2 = 4510 = 15^2 + ... + 25^2.

%t LinearRecurrence[{179,-179,1},{28,5308,945148},30] (* _Harvey P. Dale_, May 16 2019 *)

%o (PARI) Vec(-4*x*(7*x^2+74*x+7)/((x-1)*(x^2-178*x+1)) + O(x^20))

%Y Cf. A157096, A262017, A262019.

%K nonn,easy

%O 1,1

%A _Colin Barker_, Sep 08 2015