A178077 A (4,-8) Somos-4 sequence.

1, 2, 4, -16, -256, -3072, -81920, -524288, 184549376, 20401094656, 3848290697216, 932385860354048, -229683580995895296, -514202991054653751296, -608004684669466821263360, -1669526556887802890269229056, -2074787505842297340730932199424, 33552176086840775798814740439891968

Offset: 0

Author

Paul Barry, May 19 2010

Keywords

• easy
• sign

Comments

Hankel transform of A178076.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..94

Programs

Magma

I:=[1,2,4,-16]; [n le 4 select I[n] else (4*Self(n-1)*Self(n-3) - 8*Self(n-2)^2)/Self(n-4): n in [1..30]]; // G. C. Greubel, Sep 18 2018

Mathematica

RecurrenceTable[{a[n] == (4*a[n-1]*a[n-3] -8*a[n-2]^2)/a[n-4], a[0] == 1, a[1] == 2, a[2] == 4, a[3] == -16}, a, {n, 0, 30}] (* G. C. Greubel, Sep 18 2018 *)

PARI

m=30; v=concat([1,2,4,-16], vector(m-4)); for(n=5, m, v[n] = ( 4*v[n-1]*v[n-3] -8*v[n-2]^2)/v[n-4]); v \\ G. C. Greubel, Sep 18 2018

Formula

a(n) = (4*a(n-1)*a(n-3) - 8*a(n-2)^2)/a(n-4), n>=4.

Extensions

More terms from G. C. Greubel, Sep 18 2018