OFFSET
0,3
COMMENTS
Hankel transform of A143013.
The sequence uniquely extends to negative indices using the bilinear recurrence. - Michael Somos, Nov 26 2025
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..109
FORMULA
a(n) = (4*a(n-1)*a(n-3) - 5*a(n-2)^2)/a(n-4), n>=3.
From Michael Somos, Nov 26 2025: (Start)
a(n) = a(-3-n) for all n in Z.
a(n-2)*a(n+2) == 4*a(n-1)*a(n+1) - 5*a(n)^2 for all n in Z.
a(n-2)*a(n+3) == 5*a(n-1)*a(n+2)- 4*a(n)*a(n+1) for all n in Z.
a(n-1) = (-1)^n*A178627(2*n+1) for all n in Z. (End)
MATHEMATICA
RecurrenceTable[{a[n] == (4*a[n-1]*a[n-3] -5*a[n-2]^2)/a[n-4], a[0] == 1, a[1] == -1, a[2] == -9, a[3] == -41}, a, {n, 0, 30}] (* G. C. Greubel, Sep 18 2018 *)
a[ n_] := Which[n<-1, a[-3-n], n<3, {1, 1, -1, -9}[[2+n]], True, a[n] = (4*a[n-1]*a[n-3] - 5*a[n-2]^2)/a[n-4]]; (* Michael Somos, Nov 26 2025 *)
PROG
(PARI) m=30; v=concat([1, -1, -9, -41], vector(m-4)); for(n=5, m, v[n] = ( 4*v[n-1]*v[n-3] -5*v[n-2]^2)/v[n-4]); v \\ G. C. Greubel, Sep 18 2018
(Magma) I:=[1, -1, -9, -41]; [n le 4 select I[n] else (4*Self(n-1)*Self(n-3) -5*Self(n-2)^2)/Self(n-4): n in [1..30]]; // G. C. Greubel, Sep 18 2018
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Paul Barry, Dec 08 2009
STATUS
approved