A247369 a(n) = (a(n-1) * a(n-3) + (-1)^n * a(n-2)^2) / a(n-4), with a(0) = 0, a(1) = -1, a(2) = a(3) = a(4) = 1, a(9) = 3.

0, -1, 1, 1, 1, 0, 1, 1, 1, 3, 4, -5, 1, -7, 9, 8, 25, -23, 49, 87, 16, 295, 529, -903, 841, -1256, 3481, -1495, 16641, -44341, 98596, 217651, 4225, 1058961, 2337841, -5106896, 13608721, 5415345, 67387681, -173830481, 264517696, -2288275633, 6941055969

Offset: 0

Author

Michael Somos, Sep 14 2014

Keywords

• sign

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..400

Crossrefs

Cf. A006769.

Programs

Haskell

a247369 n = a247369_list !! n
a247369_list = [0, -1, 1, 1, 1, 0] ++ xs where
   xs = [1, 1, 1, 3] ++ zipWith (flip div) xs (zipWith (+)
              (zipWith (*) (tail xs) (drop 3 xs))
              (zipWith (*) (cycle [1, -1]) (map (^ 2) $ drop 2 xs)))
-- Reinhard Zumkeller, Sep 15 2014

Magma

I:=[3, 4, -5, 1]; [0, -1, 1, 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

Mathematica

Join[{0, -1, 1, 1, 1, 0, 1, 1, 1}, RecurrenceTable[{a[9]==3, a[10]==4, a[11]==-5, a[12]==1, a[n]==(a[n-1]a[n-3] + (-1)^n a[n-2]^2)/a[n-4]}, a, {n, 9, 30}]] (* G. C. Greubel, Aug 05 2018 *)

PARI

{a(n) = my(A = [-1, 1, 1, 1]); n=abs(n); if( n==0, 0, if( n<5, A[n], A = concat(A, vector(n-4)); for(k=5, n, A[k] = if( k==9, 3, (A[k-1] * A[k-3] + (-1)^k * A[k-2]^2) / A[k-4])); A[n]))};

Formula

0 = a(n)*a(n+9) + a(n+1)*a(n+8) + a(n+3)*a(n+6) + a(n+4)*a(n+5) for all n in Z.

a(n) = a(-n), a(2*n) = A006769(n)^2 for all n in Z.