A235789 Expansion of x * (1 - 2*x + 8*x^5 - 8*x^6) / (1 - 4*x^4)^2.

0, 1, -2, 0, 0, 8, -8, -8, 0, 48, -32, -64, 0, 256, -128, -384, 0, 1280, -512, -2048, 0, 6144, -2048, -10240, 0, 28672, -8192, -49152, 0, 131072, -32768, -229376, 0, 589824, -131072, -1048576, 0, 2621440, -524288, -4718592, 0, 11534336, -2097152, -20971520, 0

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..2500

Index entries for linear recurrences with constant coefficients, signature (0, -2, 0, 4, 0, 8).

Formula

0 = a(n) * (n^2 + 5*n + 14) + a(n+1) * (-4) + a(n+2) * (-n-2) + a(n+3) * (2) + a(n+4) * (-n^2 - 3*n - 10)/4 for all n in Z.

0 = a(n) * (4*a(n+1) + 2*a(n+2)) + a(n+1) * (2*a(n+1) + 3*a(n+2) + a(n+3)) + a(n+2) * (a(n+2) + a(n+3)) for all n in Z.

a(-n) = a(n) / 2^n. a(4*n) = 0. a(4*n + 2) = -(2^(2*n + 1)). a(4*n + 3) = -n * 2^(2*n + 1). a(4*n + 1) = (n+1) * 2^(2*n).

Example

G.f. = x - 2*x^2 + 8*x^5 - 8*x^6 - 8*x^7 + 48*x^9 - 32*x^10 - 64*x^11 + ...

Mathematica

CoefficientList[Series[x*(1-2*x+8*x^5-8*x^6)/(1-4*x^4)^2, {x, 0, 50}], x] (* G. C. Greubel, Aug 07 2018 *)
LinearRecurrence[{0, -2, 0, 4, 0, 8}, {0, 1, -2, 0, 0, 8}, 50] (* Harvey P. Dale, Jul 23 2020 *)

Prog

(PARI) {a(n) = [0, (n+3)/4, -1, -(n-3)/4] [n%4 + 1] * 2^(n\2)}
(PARI) x='x+O('x^50); concat([0], Vec(x*(1-2*x+8*x^5-8*x^6)/(1-4*x^4)^2)) \\ G. C. Greubel, Aug 07 2018
(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!(x*(1-2*x+8*x^5-8*x^6)/(1-4*x^4)^2)); // G. C. Greubel, Aug 07 2018

Crossrefs

Sequence in context: A230910 A215122 A332473 * A236925 A134414 A113036

Adjacent sequences: A235786 A235787 A235788 * A235790 A235791 A235792

Keyword

sign

Author

Michael Somos, Jan 15 2014

Status

approved