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A131183
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a(n) = a(n-1) + a(n-2) if n == 3 mod 4; a(n) = a(n-1) - a(n-2) if n == 0 mod 4; a(n) = a(n-1)*a(n-2) if n == 1 mod 4; and a(n) = a(n-1)/a(n-2) if n == 2 mod 4; with a(1)=a(2)=1.
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2
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1, 1, 2, 1, 2, 2, 4, 2, 8, 4, 12, 8, 96, 12, 108, 96, 10368, 108, 10476, 10368, 108615168, 10476, 108625644, 108615168, 11798392572168192, 108625644, 11798392680793836, 11798392572168192, 139202068568601556987554268864512
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OFFSET
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1,3
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COMMENTS
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If S(n)=a(4n-1) (i.e., term "+"), R(n)=a(4n) (i.e., "-"), P(n)=a(4n+1), D(n)=a(4n+2) then D(n)=S(n), P(n)=S(n+1)-S(n), R(n+1)=P(n)=S(n+1)-S(n). - Jose Ramon Real, Nov 10 2007
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LINKS
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EXAMPLE
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a(3) = a(2) + a(1) = 1 + 1 = 2;
a(4) = a(3) - a(2) = 2 - 1 = 1;
a(5) = a(4) * a(3) = 1 * 2 = 2;
a(6) = a(5) / a(4) = 2 / 1 = 2.
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MAPLE
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MATHEMATICA
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a[1]=a[2]=1; a[n_] := a[n] = Switch[Mod[n, 4], 3, a[n-1]+a[n-2], 0, a[n-1]-a[n-2], 1, a[n-1]*a[n-2], 2, a[n-3]]; Array[a, 30] (* Jean-François Alcover, Dec 28 2015 *)
nxt[{n_, a_, b_}]:=Module[{m=Mod[n+1, 4]}, {n+1, b, Which[m==3, a+b, m==0, b-a, m==1, a*b, m==2, b/a]}]; Join[{1, 1, 2}, NestList[nxt, {1, 1, 2}, 30][[All, 2]]] (* Harvey P. Dale, Sep 04 2017 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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