A236172 a(n) = ( a(n-2)*(3*a(n-3) + a(n-2)) + a(n-1)*(a(n-1) + 2*a(n-2) + a(n-3)) ) / ( 2*a(n-3) - a(n-2) - 3*a(n-1) ), with a(0)=-3, a(1)=1, a(2)=-2, a(3)=2.

-3, 1, -2, 2, 2, 0, 8, -4, 4, -8, 0, -2, -2, 2, -1, 3, -1, 2, -2, -2, 0, -8, 4, -4, 8, 0, 2, 2, -2, 1, -3, 1, -2, 2, 2, 0, 8, -4, 4, -8, 0, -2, -2, 2, -1, 3, -1, 2, -2, -2, 0, -8, 4, -4, 8, 0, 2, 2, -2, 1, -3, 1, -2, 2, 2, 0, 8, -4, 4, -8, 0, -2, -2, 2, -1, 3

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 (0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1).

Formula

G.f.: (-3 + x - 2*x^2 + 2*x^3 + 2*x^4 + 8*x^6 - 4*x^7 + 4*x^8 - 8*x^9 - 2*x^11 - 2*x^12 + 2*x^13 - x^14) / (1 + x^15).

a(n) = -a(n + 15) = a(n + 30) = a(-n) for all n in Z.

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

Example

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

Mathematica

CoefficientList[Series[(-3+x-2*x^2+2*x^3+2*x^4+8*x^6-4*x^7+ 4*x^8-8*x^9 - 2*x^11-2*x^12+2*x^13-x^14)/(1+x^15), {x, 0, 60}], x] (* G. C. Greubel, Aug 07 2018 *)

Prog

(PARI) {a(n) = (-1)^(n\15) * [-3, 1, -2, 2, 2, 0, 8, -4, 4, -8, 0, -2, -2, 2, -1][n%15 + 1]};
(PARI) x='x+O('x^60); Vec((-3+x-2*x^2+2*x^3+2*x^4+8*x^6-4*x^7+ 4*x^8- 8*x^9-2*x^11-2*x^12+2*x^13-x^14)/(1+x^15)) \\ G. C. Greubel, Aug 07 2018
(Magma) m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((-3+x-2*x^2+2*x^3+2*x^4+8*x^6-4*x^7+ 4*x^8-8*x^9 - 2*x^11-2*x^12 +2*x^13-x^14)/(1+x^15))); // G. C. Greubel, Aug 07 2018

Crossrefs

Sequence in context: A327314 A021888 A115310 * A139381 A225849 A038575

Adjacent sequences: A236169 A236170 A236171 * A236173 A236174 A236175

Keyword

sign,easy

Author

Michael Somos, Jan 19 2014

Status

approved