A247370 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.

1, 1, 0, 1, 1, 1, 2, 3, -1, 7, 10, 13, 9, 37, 40, 133, 369, 877, -488, 4429, 9881, 16869, 46970, 169039, 65311, 1875739, 6659730, 23387209, -7406159, 265302649, 923436432, 2717142457, 17805417409, 89803227913, -79079320720, 2449845576777, 12004801505489

Offset

0,7

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..300

Formula

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.

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.

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.

a(-n) = a(n) for all n in Z.

Mathematica

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 *)

Prog

(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)))};
(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])};
(Haskell)
a247370 n = a247370_list !! n
a247370_list = [1, 1, 0] ++ xs where
   xs = [1, 1, 1, 2] ++ zipWith (flip div) xs (zipWith (+)
              (zipWith (*) (tail xs) (drop 3 xs))
              (zipWith (*) (cycle [1, -1]) (map (^ 2) $ drop 2 xs)))
-- Reinhard Zumkeller, Sep 17 2014
(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

Crossrefs

Sequence in context: A173459 A354839 A121637 * A161847 A101175 A050512

Adjacent sequences: A247367 A247368 A247369 * A247371 A247372 A247373

Keyword

sign

Author

Michael Somos, Sep 14 2014

Status

approved