A284985 - OEIS

%I #19 Jul 16 2024 14:22:44

%S 0,24,13824,7962600,4586443776,2641783652376,1521662797324800,

%T 876475129475432424,504848152915051751424,290791659603940333387800,

%U 167495491083716716979621376,96477112072561225039928524776,55570649058304181906281850649600

%N a(0)=0, a(1)=24; for n>=2, a(n)=576*a(n-1)-a(n-2).

%C a(n-1) and a(n+1) are the solutions for c if b=a(n) in (b^2+c^2)/(b*c+1)=576 and there are no other pairs of solutions apart from consecutive pairs of terms in this sequence.

%H Colin Barker, <a href="/A284985/b284985.txt">Table of n, a(n) for n = 0..350</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (576,-1).

%F a(n) = 576*a(n-1)-a(n-2).

%F a(n) = 12/(17*sqrt(287))*(((-1/(288+17287))^(n))+((288+(17*sqrt(287)))^(n))).

%F G.f.: 24*x/(1-576*x+x^2) . - _R. J. Mathar_, Apr 10 2017

%t nxt[{a_,b_}]:={b,576b-a}; NestList[nxt,{0,24},20][[;;,1]] (* or *) LinearRecurrence[{576,-1},{0,24},20] (* _Harvey P. Dale_, Jul 16 2024 *)

%o (PARI) concat(0, Vec(24*x/(1-576*x+x^2) + O(x^20))) \\ _Colin Barker_, Apr 10 2017

%Y Cf. A052530.

%K nonn,easy,less

%O 0,2

%A _Kyle Degen_, Apr 06 2017

%E a(8)-a(12) from _Giovanni Resta_, Apr 10 2017