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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
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, -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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

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.

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

REFERENCES

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

LINKS

Table of n, a(n) for n=1..88.

FORMULA

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).

MATHEMATICA

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}]

CROSSREFS

Sequence in context: A123551 A286275 A029717 * A105972 A305024 A064134

Adjacent sequences:  A135564 A135565 A135566 * A135568 A135569 A135570

KEYWORD

uned,sign

AUTHOR

Roger L. Bagula, Feb 23 2008

STATUS

approved

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Last modified November 19 20:42 EST 2019. Contains 329323 sequences. (Running on oeis4.)