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A061292 a(n) = a(n-1)*a(n-2)*a(n-3) - a(n-4) for n>3 with a(0) = a(1) = a(2) = a(3) = 2.

%I A061292 #39 Jun 18 2025 11:14:46
%S A061292 2,2,2,2,6,22,262,34582,199330642,1806032092550706,
%T A061292 12449434806576800059248920402,
%U A061292 4481765860945171681908664776799089162954814190172722
%N A061292 a(n) = a(n-1)*a(n-2)*a(n-3) - a(n-4) for n>3 with a(0) = a(1) = a(2) = a(3) = 2.
%C A061292 Any four consecutive terms are a solution to the Diophantine equation w^2 + x^2 + y^2 + z^2 = wxyz.
%C A061292 a(n) = 2 * A072878(n+1).
%H A061292 Vincenzo Librandi, <a href="/A061292/b061292.txt">Table of n, a(n) for n = 0..18</a>
%H A061292 Michael Magee and Brady Haran, <a href="https://youtube.com/watch?v=a7BVL1MOCl4">A simple equation that behaves weirdly</a>, Numberphile, Youtube video, 2025.
%t A061292 a[1] := 2; a[2] := 2; a[3] := 2; a[4] := 2; a[n_] := a[n - 1]*a[n - 2]*a[n - 3] - a[n - 4]; Table[a[n], {n, 1, 15}] (* _Stefan Steinerberger_, Mar 31 2006 *)
%t A061292 RecurrenceTable[{a[0]==a[1]==a[2]==a[3]==2,a[n]==a[n-1]a[n-2]a[n-3]- a[n-4]},a[n],{n,12}] (* _Harvey P. Dale_, Sep 15 2011 *)
%o A061292 (Magma) I:=[2,2,2,2]; [n le 4 select I[n] else Self(n-1)*Self(n-2)*Self(n-3)-Self(n-4): n in [1..12]]; // _Vincenzo Librandi_, Sep 17 2011
%o A061292 (Haskell)
%o A061292 a061292 n = a061292_list !! n
%o A061292 a061292_list = 2 : 2 : 2 : 2 : zipWith (-)
%o A061292    (zipWith3 (((*) .) . (*)) (drop 2 xs) (tail xs) xs) a061292_list
%o A061292    where xs = tail a061292_list
%o A061292 -- _Reinhard Zumkeller_, Mar 25 2015
%Y A061292 Cf. A022405, A061021, A072878, A072879, A072880.
%K A061292 easy,nonn,nice
%O A061292 0,1
%A A061292 _Stephen G Penrice_, Jun 04 2001
%E A061292 More terms from Larry Reeves (larryr(AT)acm.org) and _Jason Earls_, Jun 05 2001