A236172 - OEIS

%I #15 Sep 08 2022 08:46:06

%S -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,

%T -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,

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

%N 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.

%H G. C. Greubel, <a href="/A236172/b236172.txt">Table of n, a(n) for n = 0..2500</a>

%H <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1).

%F 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).

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

%F 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.

%e 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 + ...

%t 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 *)

%o (PARI) {a(n) = (-1)^(n\15) * [-3, 1, -2, 2, 2, 0, 8, -4, 4, -8, 0, -2, -2, 2, -1][n%15 + 1]};

%o (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

%o (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

%K sign,easy

%O 0,1

%A _Michael Somos_, Jan 19 2014