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A131183 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.

%I A131183 #17 Sep 04 2017 15:58:42
%S A131183 1,1,2,1,2,2,4,2,8,4,12,8,96,12,108,96,10368,108,10476,10368,
%T A131183 108615168,10476,108625644,108615168,11798392572168192,108625644,
%U A131183 11798392680793836,11798392572168192,139202068568601556987554268864512
%N A131183 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.
%C A131183 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
%e A131183 a(3) = a(2) + a(1) = 1 + 1 = 2;
%e A131183 a(4) = a(3) - a(2) = 2 - 1 = 1;
%e A131183 a(5) = a(4) * a(3) = 1 * 2 = 2;
%e A131183 a(6) = a(5) / a(4) = 2 / 1 = 2.
%p A131183 A131183 := proc(n) option remember ; if n <= 2 then 1 ; elif n mod 4 = 3 then A131183(n-1)+A131183(n-2) ; elif n mod 4 = 0 then A131183(n-1)-A131183(n-2) ; elif n mod 4 = 1 then A131183(n-1)*A131183(n-2) ; else A131183(n-1)/A131183(n-2) ; fi ; end: seq(A131183(n),n=1..35) ; # _R. J. Mathar_, Oct 28 2007
%t A131183 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 *)
%t A131183 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 *)
%K A131183 easy,nonn
%O A131183 1,3
%A A131183 _Jose Ramon Real_, Oct 22 2007
%E A131183 More terms from _R. J. Mathar_, Oct 28 2007