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

Offset: 0

Author

Kyle Degen, Apr 06 2017

Keywords

• nonn
• easy
• less

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).

Crossrefs

Cf. A052530.

Programs

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 *)

PARI

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

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

Extensions

a(8)-a(12) from Giovanni Resta, Apr 10 2017