A247487 Expansion of (2 + x + x^2 + x^3 - x^4 - 2*x^5 - 4*x^6 - 8*x^7) / (1 - x^4 + 16*x^8) in powers of x.

2, 1, 1, 1, 1, -1, -3, -7, -31, -17, -19, -23, -47, -1, 29, 89, 449, 271, 333, 457, 1201, 287, -131, -967, -5983, -4049, -5459, -8279, -25199, -8641, -3363, 7193, 70529, 56143, 83981, 139657, 473713, 194399, 137789, 24569, -654751, -703889, -1205907, -2209943

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,1,0,0,0,-16).

Formula

a(n) = a(-n) * 2^n = a(n-4) - 16*a(n-8) for all n in Z.

a(2*n + 1) = (-1)^n * A087168(n).

A247518(n) = a(n+1) * a(n) * a(n-1) * a(n-2) for all n in Z.

Example

G.f. = 2 + x + x^2 + x^3 + x^4 - x^5 - 3*x^6 - 7*x^7 - 31*x^8 - 17*x^9 + ...

Maple

seq(coeff(series((2+x+x^2+x^3-x^4-2*x^5-4*x^6-8*x^7)/(1-x^4+16*x^8), x, n+1), x, n), n=0..50); # Muniru A Asiru, Aug 05 2018

Mathematica

CoefficientList[Series[(2+x+x^2+x^3-x^4-2*x^5-4*x^6-8*x^7)/(1 -x^4 + 16*x^8), {x, 0, 60}], x]] (* G. C. Greubel, Aug 05 2018 *)

Prog

(PARI) {a(n) = if( n<0, n=-n; 2^-n, 1) * polcoeff( (2 + x + x^2 + x^3 - x^4 - 2*x^5 - 4*x^6 - 8*x^7) / (1 - x^4 + 16*x^8) + x * O(x^n), n)};
(Magma) m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((2+x+x^2+x^3-x^4-2*x^5-4*x^6-8*x^7)/(1-x^4+16*x^8))); // G. C. Greubel, Aug 05 2018
(GAP) a:=[2, 1, 1, 1, 1, -1, -3, -7];; for n in [9..50] do a[n]:=a[n-4]-16*a[n-8]; od; a; # Muniru A Asiru, Aug 05 2018

Crossrefs

CF. A087168, A247518.

Sequence in context: A060176 A305297 A218220 * A010248 A325403 A132068

Adjacent sequences: A247484 A247485 A247486 * A247488 A247489 A247490

Keyword

sign,easy

Author

Michael Somos, Sep 18 2014

Status

approved