A247368 a(n) = (a(n-1) * a(n-3) - (-1)^n * a(n-2)^2) / a(n-4) with a(0) = 0, a(1) = ... = a(4) = 1.

0, 1, 1, 1, 1, 2, 1, 5, 9, 17, 4, 65, 121, 277, 841, 2746, 441, 28561, 93025, 312001, 583696, 5309441, 14145121, 116815697, 719795241, 4487760170, 433763929, 175081030037, 1091329140889, 6935920173025, 53828252727076, 610296440614897, 1223724862004841

Offset: 0

Author

Michael Somos, Sep 14 2014

Keywords

• nonn

Comments

This is similar to Somos-4 (A006720) except for the alternating coefficient of a(n-2)^2.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..250

Crossrefs

Cf. A178384.

Programs

Haskell

a247368 n = a247368_list !! n
a247368_list = 0 : xs where
   xs = [1, 1, 1, 1] ++ 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:=[1, 1, 1, 1]; [0] 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}, RecurrenceTable[{a[1]==1, a[2]==1, a[3]==1, a[4]==1, a[n]==(a[n-1]a[n-3] - (-1)^n a[n-2]^2)/a[n-4]}, a, {n,4, 30}]] (* G. C. Greubel, Aug 05 2018 *)

PARI

{a(n) = n=abs(n); if( n<5, n>0, (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>0, A = vector(n, k, 1); for(k=5, n, A[k] = (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) - 3*a(n+3)*a(n+6) - 3*a(n+4)*a(n+5) for all n in Z.

a(n) = a(-n), a(2*n) = A178384(n)^2 for all n in Z.