OFFSET
0,10
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 0..400
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.
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 *)
PROG
(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]))};
(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
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Sep 14 2014
STATUS
approved