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%I #10 Sep 08 2022 08:46:09
%S 1,1,0,1,1,1,2,3,-1,7,10,13,9,37,40,133,369,877,-488,4429,9881,16869,
%T 46970,169039,65311,1875739,6659730,23387209,-7406159,265302649,
%U 923436432,2717142457,17805417409,89803227913,-79079320720,2449845576777,12004801505489
%N a(n) = (a(n-1) * a(n-3) - (-1)^n * a(n-2)^2) / a(n-4) with a(0) = 1, a(1) = 1, a(2) = 0, a(3) = 1, a(6) = 2.
%H Reinhard Zumkeller, <a href="/A247370/b247370.txt">Table of n, a(n) for n = 0..300</a>
%F 0 = a(n)*a(n+4) - a(n+1)*a(n+3) + (-1)^n*a(n+2)*a(n+2) for all n in Z.
%F 0 = a(n)*a(n+9) + a(n+1)*a(n+8) - 2*a(n+3)*a(n+6) - 2*a(n+4)*a(n+5) for all n in Z.
%F 0 = a(n)*a(n+12) - 2*a(n+2)*a(n+10) + a(n+4)*a(n+8) - 2*a(n+6)*a(n+6) for all n in Z.
%F a(-n) = a(n) for all n in Z.
%t Join[{1,1,0,1,1,1}, RecurrenceTable[{a[6]==2, a[7]==3, a[8]==-1, a[9]==7, a[n]==(a[n-1]a[n-3] - (-1)^n a[n-2]^2)/a[n-4]}, a, {n, 6, 30}]] (* _G. C. Greubel_, Aug 05 2018 *)
%o (PARI) {a(n) = n=abs(n); if( n<5, n!=2, if( n==6, 2, (a(n-1) * a(n-3) - (-1)^n * a(n-2)^2) / a(n-4)))};
%o (PARI) {a(n) = my(A); n=abs(n); if( n<5, n!=2, A = vector(n, k, 1); A[2]=0; for(k=5, n, A[k] = if( k==6, 2, (A[k-1] * A[k-3] - (-1)^k * A[k-2]^2) / A[k-4])); A[n])};
%o (Haskell)
%o a247370 n = a247370_list !! n
%o a247370_list = [1, 1, 0] ++ xs where
%o xs = [1, 1, 1, 2] ++ zipWith (flip div) xs (zipWith (+)
%o (zipWith (*) (tail xs) (drop 3 xs))
%o (zipWith (*) (cycle [1, -1]) (map (^ 2) $ drop 2 xs)))
%o -- _Reinhard Zumkeller_, Sep 17 2014
%o (Magma) I:=[2,3,-1,7]; [1,1,0,1,1,1] cat [n le 4 select I[n] else ( Self(n-1)*Self(n-3) + (-1)^n*Self(n-2)^2 )/Self(n-4): n in [1..30]]; // _G. C. Greubel_, Aug 05 2018
%K sign
%O 0,7
%A _Michael Somos_, Sep 14 2014
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