A162546 A Somos-4 variant: a(n) = (36*a(n-1)*a(n-3) - 68*a(n-2)^2)/a(n-4).

1, 1, -16, -644, -40592, -4821056, 17059328, 2492895195136, 10659285907800064, 86296767700623425536, 1081586547380924161458176, -36649408809924048998874742784, -18144416387824430577315746611724288

Offset: 0

Author

Paul Barry, Jul 05 2009

Keywords

• easy
• sign

Comments

Hankel transform of A162543, A162548.

Links

• Fung Lam, Table of n, a(n) for n = 0..67

Crossrefs

Cf. A157005, A157101, A162547.

Programs

GAP

a:=[1,1,-16,-644];; for n in [5..20] do a[n]:=(36*a[n-1]*a[n-3] - 68*a[n-2]^2)/a[n-4]; od; a; # G. C. Greubel, Feb 23 2019

Magma

I:=[1,1,-16,-644]; [n le 4 select I[n] else (36*Self(n-1) *Self(n-3) - 68*Self(n-2)^2)/Self(n-4): n in [1..20]]; // G. C. Greubel, Feb 23 2019

Mathematica

RecurrenceTable[{a[n]==(36*a[n-1]*a[n-3] - 68*a[n-2]^2)/a[n-4], a[0]==1, a[1]==1, a[2]==-16, a[3]==-644}, a, {n,20}] (* G. C. Greubel, Feb 23 2019 *)

PARI

m=20; v=concat([1,1,-16,-644], vector(m-4)); for(n=5, m, v[n] = (36*v[n-1]*v[n-3] -68*v[n-2]^2)/v[n-4]); v \\ G. C. Greubel, Feb 23 2019

Sage

def a(n):
    if (n==0): return 1
    elif (n==1): return 1
    elif (n==2): return -16
    elif (n==3): return -644
    else: return (36*a(n-1)*a(n-3) - 68*a(n-2)^2)/a(n-4)
[a(n) for n in (1..20)] # G. C. Greubel, Feb 23 2019