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%I #18 Apr 07 2018 15:23:02
%S 0,1,2,2,1,-1,-2,-1,1,3,4,3,0,-3,-3,0,3,6,6,3,-3,-6,-3,3,9,12,9,0,-9,
%T -9,0,9,18,18,9,-9,-18,-9,9,27,36,27,0,-27,-27,0,27,54,54,27,-27,-54,
%U -27,27,81,108,81,0,-81,-81,0,81,162,162,81,-81,-162,-81,81,243,324,243,0
%N a(0)=0, a(1)=1, a(2)=2. For n >= 3, a(n) = a(n-1) - min(a(n-2), a(n-3)).
%C a(n+15) = 3*a(n) for all n. - Dion Gijswijt (gijswijt(AT)science.uva.nl) Jul 29 2009 on SeqFan mailing list.
%H A. Karttunen, <a href="/A163495/b163495.txt">Table of n, a(n) for n=0..224</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, 3).
%F G.f. x*(1 +2*x +2*x^2 +x^3 -x^4 -2*x^5 -x^6 +x^7 +3*x^8 +4*x^9 +3*x^10 -3*x^12 -3*x^13) / (1 - 3*x^15 ). - _R. J. Mathar_, Jun 22 2011
%p a[0] := 0: a[1] := 1: a[2] := 2: for n from 3 to 80 do a[n] := a[n-1]-min(a[n-2], a[n-3]) end do: seq(a[n], n = 0 .. 80); # _Emeric Deutsch_, Aug 01 2009
%t CoefficientList[Series[x*(1 +2*x +2*x^2 +x^3 -x^4 -2*x^5 -x^6 +x^7 +3*x^8 +4*x^9 +3*x^10 -3*x^12 -3*x^13)/(1 - 3*x^15 ), {x, 0, 50}], x] (* _G. C. Greubel_, Jul 26 2017 *)
%t nxt[{a_,b_,c_}]:={b,c,c-Min[a,b]}; NestList[nxt,{0,1,2},80][[All,1]] (* or *) LinearRecurrence[{0,0,0,0,0,0,0,0,0,0,0,0,0,0,3},{0,1,2,2,1,-1,-2,-1,1,3,4,3,0,-3,-3},80] (* _Harvey P. Dale_, Apr 07 2018 *)
%o (PARI) x='x+O('x^50); concat([0], Vec(x*(1 +2*x +2*x^2 +x^3 -x^4 -2*x^5 -x^6 +x^7 +3*x^8 +4*x^9 +3*x^10 -3*x^12 -3*x^13)/(1 - 3*x^15 ))) \\ _G. C. Greubel_, Jul 26 2017
%K sign
%O 0,3
%A _Leroy Quet_, Jul 29 2009
%E Extended by _Emeric Deutsch_, Aug 01 2009
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