OFFSET
0,6
COMMENTS
Essentially a (1,-1) Somos-4 sequence.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..150
FORMULA
a(n) = (a(n-1)*a(n-3) - a(n-2)^2)/a(n-4), n>=6.
a(n) = -a(2-n), a(n)*a(n+5) = a(n+1)*a(n+4) - 2*a(n+2)*a(n+3) for all n in Z. - Michael Somos, Sep 26 2018
MATHEMATICA
nxt[{a_, b_, c_, d_}]:={b, c, d, (d*b-c^2)/a}; Join[{1, 0}, NestList[nxt, {-1, -1, -1, -2}, 30][[All, 1]]] (* Harvey P. Dale, Sep 07 2017 *)
Join[{1, 0}, RecurrenceTable[{a[n] == (a[n-1]*a[n-3] -a[n-2]^2)/a[n-4], a[2] == -1, a[3] == -1, a[4] == -1, a[5] == -2}, a, {n, 2, 50}]] (* G. C. Greubel, Sep 25 2018 *)
PROG
(PARI) m=20; v=concat([-1, -1, -1, -2], vector(m-4)); for(n=5, m, v[n] = ( 100*v[n-1]*v[n-3] - 196*v[n-2]^2)/v[n-4]); concat([1, 0], v) \\ G. C. Greubel, Sep 25 2018
(Magma) I:=[-1, -1, -1, -2]; [1, 0] cat [n le 4 select I[n] else (Self(n-1)*Self(n-3) - Self(n-2)^2)/Self(n-4): n in [1..20]]; // G. C. Greubel, Sep 25 2018
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Paul Barry, Mar 18 2010
STATUS
approved