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A089983
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1, 1, 1, 1, ... a, b, c, d, ab-cd, ...
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1
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1, 1, 1, 1, 0, 1, 1, -1, 1, 2, -3, 5, 17, -91, 1532, 139497, -213710951, 29812036392235, 6371158648631364574889, -189937213493701003981668660072118562, 1210120120447335073097142485947209203511752911347585124133
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,10
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COMMENTS
| Inspired by the formula for the determinant of a 2 X 2 matrix.
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 (benoit7848c(AT)orange.fr), Nov 19 2003
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FORMULA
| 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).
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 (benoit7848c(AT)orange.fr), Nov 19 2003
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PROG
| (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, ", "))
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CROSSREFS
| Cf. A089984.
Sequence in context: A173236 A082979 A065952 * A072858 A087911 A099936
Adjacent sequences: A089980 A089981 A089982 * A089984 A089985 A089986
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KEYWORD
| sign,easy
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AUTHOR
| Ray Chandler (rayjchandler(AT)sbcglobal.net), following a suggestion of Rainer Rosenthal (r.rosenthal(AT)web.de), Nov 18 2003
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