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A089984
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1, 1, 1, 1, ... a, b, c, d, ac-bd, ...
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1
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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, -226573, 45538573, -105193879657, -23833987746960404, 1085365814730154781188953, 114173840897460294190477827374165629, 272121792497347519357684708535661864450
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,15
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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, 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 (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-2)-a(n-3)*a(n-1).
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 (benoit7848c(AT)orange.fr), Nov 19 2003
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PROG
| (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, ", "))
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CROSSREFS
| Cf. A089983.
Sequence in context: A085189 A130466 A129322 * A062105 A093412 A119355
Adjacent sequences: A089981 A089982 A089983 * A089985 A089986 A089987
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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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