OFFSET
0,3
COMMENTS
Hankel transform of the sequence with g.f. 1/(1-x^2/(1+2x^2/(1+(3/4)x^2/(1-(10/9)x^2/(1-...,
where -2,-3/4,10/9,... are the x-coordinates of the multiples of (0,0).
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..154
Paul Barry, Generalized Catalan recurrences, Riordan arrays, elliptic curves, and orthogonal polynomials, arXiv:1910.00875 [math.CO], 2019.
FORMULA
a(n) = (-a(n-1)*a(n-3) - 2*a(n-2)^2)/a(n-4), n>3.
MATHEMATICA
RecurrenceTable[{a[n]==(-a[n-1]*a[n-3] -2*a[n-2]^2)/a[n-4], a[0] == 1, a[1] == 1, a[2] == -2, a[3] == -3}, a, {n, 0, 30}] (* G. C. Greubel, Sep 16 2018 *)
PROG
(PARI) m=30; v=concat([1, 1, -2, -3], vector(m-4)); for(n=5, m, v[n] = ( -v[n-1]*v[n-3] - 2*v[n-2]^2)/v[n-4]); v \\ G. C. Greubel, Sep 16 2018
(Magma) I:=[1, 1, -2, -3]; [n le 4 select I[n] else (-Self(n-1)*Self(n-3) - 2*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 26 2010
STATUS
approved