OFFSET
1,4
COMMENTS
Hankel transform of the sequence with g.f. 1/(1-x^2/(1-x^2/(1-4x^2/(1+(3/16)x^2/(1-(76/9)x^2/(1-.... where 1,4,-3/16,76/9,... are the x-coordinates of the multiples of (0,0).
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..156 (offset adapted by Georg Fischer, Jan 31 2019).
FORMULA
a(n) = (-a(n-1)*a(n-3) + a(n-2)^2)/a(n-4), n>3.
a(n) = -(-1)^n*a(-n) for all n in Z. - Michael Somos, Sep 17 2018
EXAMPLE
G.f. = x + x^2 + x^3 + 4*x^4 - 3*x^5 + 19*x^6 - 67*x^7 + ... - Michael Somos, Sep 17 2018
MATHEMATICA
RecurrenceTable[{a[n] == (-a[n-1]*a[n-3] +a[n-2]^2)/a[n-4], a[0] == 1, a[1] == 1, a[2] == 1, a[3] == 4}, a, {n, 0, 30}] (* G. C. Greubel, Sep 16 2018 *)
PROG
(PARI) m=30; v=concat([1, 1, 1, 4], vector(m-4)); for(n=5, m, v[n] = ( -v[n-1]*v[n-3] +v[n-2]^2)/v[n-4]); v \\ G. C. Greubel, Sep 16 2018
(Magma) I:=[1, 1, 1, 4]; [n le 4 select I[n] else (-Self(n-1)*Self(n-3) + Self(n-2)^2)/Self(n-4): n in [1..30]]; // G. C. Greubel, Sep 16 2018
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Paul Barry, May 27 2010
EXTENSIONS
Changed offset to 1 by Michael Somos, Sep 17 2018
STATUS
approved