A145528 - OEIS

%I #20 Jan 03 2024 23:45:52

%S 455,728182,1058842239,1539555953390,2238513297452887,

%T 3254796794940610374,4732472301330350096975,6881011471337534100457342,

%U 10004985946852473251714944359,14547242685712024770459428706710

%N Numbers x such that (x+91)^3 - x^3 is a square.

%H Robert Israel, <a href="/A145528/b145528.txt">Table of n, a(n) for n = 1..316</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1455, -1455, 1).

%F a(n+2)=1454*a(n+1)-a(n)+66066.

%F a(1)=455, a(2)=728182, a(3)=1058842239, a(n)=1455*a(n-1)-1455*a(n-2)+ a(n-3). - _Harvey P. Dale_, Jun 22 2011

%F G.f.: (91*x*(-5-727*x+6*x^2))/(-1+1455*x-1455*x^2+x^3). - _Harvey P. Dale_, Jun 22 2011

%e a(1)=455 because the first relation is (455+91)^3 - 455^3 = 8281^2.

%p f:= gfun:-rectoproc({a(n+2)=1454*a(n+1)-a(n)+66066,a(1)=455,a(2)=728182},a(n),remember):

%p map(f, [$1..20]); # _Robert Israel_, Sep 24 2017

%t LinearRecurrence[{1455,-1455,1},{455,728182,1058842239},20] (* or *) CoefficientList[Series[(91 (-5-727 x+6 x^2))/(-1+1455 x-1455 x^2+x^3),{x,0,20}],x] (* _Harvey P. Dale_, Jun 22 2011 *)

%K easy,nonn

%O 1,1

%A _Richard Choulet_, Oct 12 2008