A174882 A (3/2,-1) Somos-4 sequence.

1, 1, -2, -8, -16, -16, 32, 128, 256, 256, -512, -2048, -4096, -4096, 8192, 32768, 65536, 65536, -131072, -524288, -1048576, -1048576, 2097152, 8388608, 16777216, 16777216, -33554432, -134217728, -268435456, -268435456

Offset

0,3

Comments

Hankel transform of A051286. a(n+2) = -(-1)^floor(n/4) * 2^A098181(n).

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,0,-16).

Formula

a(n) = ((3/2)*a(n-1)*a(n-3) - a(n-2)^2)/a(n-4), n>3.

a(-n) = a(n-1) / 2^(2*n - 1) for all n in Z. - Michael Somos, Jan 06 2011

0 = a(n)*(+2*a(n+4)) + a(n+1)*(-3*a(n+3)) + a(n+2)*(+2*a(n+2)) for all n in Z. - Michael Somos, Sep 18 2014

a(n+4) = -16 * a(n) for all n in Z. - Michael Somos, Sep 02 2015

G.f.: -(2*x-1)*(4*x^2+3*x+1)/(1+16*x^4) . - R. J. Mathar, Aug 18 2017

Example

G.f. = 1 + x - 2*x^2 - 8*x^3 - 16*x^4 - 16*x^5 + 32*x^6 + 128*x^7 + ...

Mathematica

a[ n_] := (-1)^Quotient[n + 2, 4] 2^(n - Mod[ Quotient[n + 1, 2], 2]); (* Michael Somos, Sep 18 2014 *)
CoefficientList[Series[(1-2*x)*(4*x^2+3*x+1)/(1+16*x^4), {x, 0, 50}], x] (* G. C. Greubel, Feb 21 2018 *)

Prog

(PARI) {a(n) = (-1)^((n+2) \ 4) * 2^(n - ((n+1) \ 2 % 2))}; /* Michael Somos, Jan 06 2011 */
(PARI) x='x+O('x^30); Vec((1-2*x)*(4*x^2+3*x+1)/(1+16*x^4)) \\ G. C. Greubel, Feb 21 2018
(Magma) Q:=Rationals(); R<x>:=PowerSeriesRing(Q, 40); Coefficients(R!((1-2*x)*(4*x^2+3*x+1)/(1+16*x^4))) // G. C. Greubel, Feb 21 2018

Crossrefs

Cf. A051286, A098181.

Sequence in context: A110004 A182039 A359228 * A080095 A193219 A213249

Adjacent sequences: A174879 A174880 A174881 * A174883 A174884 A174885

Keyword

easy,sign

Author

Paul Barry, Mar 31 2010

Status

approved