A243005 a(n) = (a(n-1) - a(n-2)) * a(n-1) / a(n-3) with a(0) = 2, a(1) = 1, a(2) = -1.

2, 1, -1, 1, 2, -2, 8, 40, -640, 54400, 74854400, -8748608000000, 1406963176644608000000, 26445277668952736475397120000000000, -79938741224658033822711947577298183091491962880000000000

Offset

0,1

Links

G. C. Greubel, Table of n, a(n) for n = 0..19

Formula

0 = a(n)*a(n+3) + a(n+1)*a(n+2) - a(n+2)*a(n+2) for all n>0.

a(n+1) = - a(n) * A243004(n) for all n>0.

a(3*n) > 0, a(3*n + 1) > 0, a(3*n + 2) < 0 for all n>=0.

Mathematica

RecurrenceTable[{a[n] == a[n - 1]*(a[n - 1] - a[n - 2])/a[n - 3],
a[0] == 2, a[1] == 1, a[2] == -1}, a, {n, 0, 15}] (* G. C. Greubel, Aug 06 2018 *)

Prog

(PARI) {a(n) = if( n<0, 0, if( n<3, [2, 1, -1][n+1], (a(n-1) - a(n-2)) * a(n-1) / a(n-3)))};
(Magma) I:=[2, 1, -1]; [n le 3 select I[n] else Self(n-1)*(Self(n-1) - Self(n-2))/Self(n-3): n in [1..15]]; // G. C. Greubel, Aug 06 2018

Crossrefs

Cf. A243004.

Sequence in context: A353524 A122520 A284995 * A058393 A131256 A362414

Adjacent sequences: A243002 A243003 A243004 * A243006 A243007 A243008

Keyword

sign

Author

Michael Somos, Aug 17 2014

Status

approved