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 A247540 a(n) = 2*a(n-1) - 3*a(n-1)^2 / a(n-2), with a(0) = a(1) = 1. 1

%I #11 Sep 08 2022 08:46:09

%S 1,1,-1,-5,65,2665,-322465,-117699725,128645799425,422086867913425,

%T -4153756867136015425,-122639671502190855423125,

%U 10862563623963550637392450625,2886411268723218638918559372525625,-2300934493386669693418957707961899750625

%N a(n) = 2*a(n-1) - 3*a(n-1)^2 / a(n-2), with a(0) = a(1) = 1.

%H Reinhard Zumkeller, <a href="/A247540/b247540.txt">Table of n, a(n) for n = 0..60</a>

%F 0 = a(n)*(-2*a(n+1) + a(n+2)) + a(n+1)*(+3*a(n+1)) for all n in Z.

%F a(n+1) = a(n) * (-1)^n * A046717(n) for all n in Z.

%F a(1-n) = (-3)^(n*(n-1)/2) / a(n) for all n in Z.

%t RecurrenceTable[{a[n] == 2*a[n-1] - 3*a[n-1]^2/a[n-2], a[0]==1, a[1]==1}, a, {n,0,30}] (* _G. C. Greubel_, Aug 04 2018 *)

%o (PARI) {a(n) = if( n<0, 1 / prod(k=1, -n, (1 + (-3)^-k) / 2), prod(k=0, n-1, (1 + (-3)^k) / 2))};

%o a247540 n = a247540_list !! n

%o a247540_list = 1 : 1 : zipWith (-)

%o (map (* 2) xs) (zipWith div (map ((* 3) . (^ 2)) xs) a247540_list)

%o where xs = tail a247540_list

%o -- _Reinhard Zumkeller_, Sep 20 2014

%o (Magma) I:=[1, 1]; [n le 2 select I[n] else 2*Self(n-1) - 3*Self(n-1)^2/Self(n-2): n in [1..30]]; // _G. C. Greubel_, Aug 04 2018

%Y Cf. A046717.

%K sign

%O 0,4

%A _Michael Somos_, Sep 18 2014

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Last modified September 18 14:18 EDT 2024. Contains 376000 sequences. (Running on oeis4.)