A174400 Hankel transform of A174399.

1, 0, -1, -1, -1, -2, -1, 3, 7, 8, 25, 37, -47, -318, -559, -2023, -7039, 496, 90431, 314775, 1139599, 8007614, 13512079, -154788437, -1247862041, -5097732072, -56844671623, -290379801907, 1403230649825, 32188159859842

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

Sequence in context: A201615 A033640 A112027 * A178079 A258987 A174254

Adjacent sequences: A174397 A174398 A174399 * A174401 A174402 A174403

Keyword

easy,sign

Author

Paul Barry, Mar 18 2010

Status

approved