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A135567 A modulo-3 second-order differential sequence of the Nørgård type designed to get a "beat" type of effect: a tristate sequence. 0

%I

%S 0,1,-1,2,4,3,-2,2,0,1,-3,1,5,-2,2,-7,2,8,5,-7,-16,-11,-10,11,11,-5,

%T -6,5,-5,3,16,6,16,-2,19,5,14,1,-20,-11,10,17,3,19,-2,2,5,0,21,9,6,22,

%U 30,1,-11,46,38,59,34,-26,-31,55,80,103,50,-49,-21,73,126,87,101,-41,-64,62,48,70,39,-29,-59,61,92,80,31,-51,-30,19,68,38

%N A modulo-3 second-order differential sequence of the Nørgård type designed to get a "beat" type of effect: a tristate sequence.

%C A tristate system like that of sunspot activity that shows a "beat" effect. The sequence is designed to be like a three-state natural chaotic system.

%C The composer Per Nørgård's name is also written in the OEIS as Per Noergaard.

%D http : // www.pernoergaard.dk/eng/strukturer/uendelig/ukonstruktion05.html

%F a0(n)=a(n-1)-(a(n-1)-2*a(n-2)+a(n-3); a1(n)=a(n-3)-(a(n-2)-2*a(n-3)+a(n-4); a2(n)=a(n-5)-(a(n-3)-2*a(n-4)+a(n-5); a(n) = If[mod[n,3]=0 then a0(n) a(n) = If[mod[n,3]=1 then a1(n) a(n) = If[mod[n,3]=2 then a2(n).

%t p[0] = 0; p[1] = 1; p[2] = -1; p[3] = p[2] + 3; p[4] = p[1] + 3; p[5] = p[0] + 3; p[i_] := p[i] = If[Mod[i, 3] == 0, p[i - 1] - (p[Floor[i/2]] - 2*p[Abs[Floor[i/2] - 1]] + p[Abs[Floor[i/2] - 2]]),If[Mod[i, 3] == 1, p[i - 3] - (p[Abs[Floor[i/2] - 2]] - 2*p[Abs[Floor[i/2] - 3]] + p[Abs[Floor[i/2] - 4]]), p[i - 5] - (p[Abs[Floor[i/2] - 3]] - 2*p[Abs[Floor[i/2] - 4]] + p[Abs[Floor[i/2] - 5]])]]; b = Table[p[n], {n, 0, 100}]

%K uned,sign

%O 1,4

%A _Roger L. Bagula_, Feb 23 2008

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Last modified October 20 03:04 EDT 2021. Contains 348099 sequences. (Running on oeis4.)