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A089984 1, 1, 1, 1, ... a, b, c, d, ac-bd, ... 1

%I

%S 1,1,1,1,0,1,-1,1,-1,0,1,1,-1,1,-2,-1,3,5,-1,-2,7,-3,-13,97,200,2309,

%T -226573,45538573,-105193879657,-23833987746960404,

%U 1085365814730154781188953,114173840897460294190477827374165629

%N 1, 1, 1, 1, ... a, b, c, d, ac-bd, ...

%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, n>4, is a periodic sequence. Letting l(p) denotes the length of the period of b(n,p) is there any rule for l(p) ? - _Benoit Cloitre_, Nov 19 2003

%F a(1)=a(2)=a(3)=a(4)=1, for n>4 a(n)=a(n-4)*a(n-2)-a(n-3)*a(n-1).

%F a(n) is asymptotic (in absolute value) to B^(r^n) where r is the real root of 1+x^2-x^3 and B>1. - _Benoit Cloitre_, Nov 19 2003

%t RecurrenceTable[{a[1]==a[2]==a[3]==a[4]==1,a[n]==a[n-4]a[n-2]- a[n-3] a[n-1]}, a,{n,40}] (* _Harvey P. Dale_, Aug 24 2019 *)

%o (PARI) a=b=c=d=1;for(n=5,30,e=b*d-a*c;a=b;b=c;c=d;d=e;print1(e,","))

%Y Cf. A089983.

%K sign,easy

%O 1,15

%A _Ray Chandler_, following a suggestion of _Rainer Rosenthal_, Nov 18 2003

%E Corrected by _Harvey P. Dale_, Aug 24 2019

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Last modified November 27 12:51 EST 2021. Contains 349394 sequences. (Running on oeis4.)