Voozh

A284985

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

0, 24, 13824, 7962600, 4586443776, 2641783652376, 1521662797324800, 876475129475432424, 504848152915051751424, 290791659603940333387800, 167495491083716716979621376, 96477112072561225039928524776, 55570649058304181906281850649600

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

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.

LINKS

Colin Barker, Table of n, a(n) for n = 0..350

Index entries for linear recurrences with constant coefficients, signature (576,-1).

FORMULA

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

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

G.f.: 24*x/(1-576*x+x^2) . - R. J. Mathar, Apr 10 2017

MATHEMATICA

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 *)

PROG

(PARI) concat(0, Vec(24*x/(1-576*x+x^2) + O(x^20))) \\ Colin Barker, Apr 10 2017

CROSSREFS