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%I #18 Sep 08 2022 08:45:12
%S 1,1,1,1,0,1,1,-1,1,2,-3,5,17,-91,1532,139497,-213710951,
%T 29812036392235,6371158648631364574889,
%U -189937213493701003981668660072118562,1210120120447335073097142485947209203511752911347585124133
%N 1, 1, 1, 1, ... a, b, c, d, ab-cd, ...
%C Inspired by the formula for the determinant of a 2 X 2 matrix.
%C Sequence b(n,p) = a(n) (mod p), p prime, is a periodic sequence. Letting l(p) denotes the length of the period of b(n,p) we get l(2)=5, l(3)=11, l(5)=31... Is there any rule for l(p) ? - _Benoit Cloitre_, Nov 19 2003
%H Harvey P. Dale, <a href="/A089983/b089983.txt">Table of n, a(n) for n = 1..26</a>
%F a(1)=a(2)=a(3)=a(4)=1, for n>4 a(n)=a(n-4)*a(n-3)-a(n-2)*a(n-1).
%F a(n) is asymptotic (in absolute value) to A^(phi^n) where phi=golden ratio and A=1.005384.. (follows same kind of behavior as A000301, A007660) - _Benoit Cloitre_, Nov 19 2003
%t nxt[{a_,b_,c_,d_}]:={b,c,d,a b-c d}; NestList[nxt,{1,1,1,1},20][[All,1]] (* _Harvey P. Dale_, Oct 30 2021 *)
%o (PARI) a=b=c=d=1;for(n=5,20,e=a*b-c*d;a=b;b=c;c=d;d=e;print1(e,","))
%o (Magma) I:=[1,1,1,1]; [n le 4 select I[n] else -Self(n-1)*Self(n-2)+Self(n-3)*Self(n-4): n in [1..22]]; // _Vincenzo Librandi_, Mar 30 2014
%Y Cf. A089984.
%K sign,easy
%O 1,10
%A _Ray Chandler_, following a suggestion of _Rainer Rosenthal_, Nov 18 2003
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