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A190783
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a(n) = (a(n-1)*a(n-4) + a(n-5)*a(n-8)) / a(n-9), a(0) = ... = a(8) = 1.
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1
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1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 11, 35, 143, 719, 7919, 138599, 6606599, 1187536349, 1880820071128, 23698161912595167, 4473264365531123929334, 37148000229053373125262814729, 97174832313033554288685856553122901797
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OFFSET
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0,10
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COMMENTS
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The recursion exhibits the Laurent phenomenon.
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LINKS
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Sergey Fomin and Andrei Zelevinsky, The Laurent phenomenon, Advances in Applied Mathematics 28 (2002), 119-144.
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FORMULA
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A078918(n) = a(n+4)*a(n+2)*a(n+1)*a(n-1).
a(8-n) = a(n).
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MATHEMATICA
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RecurrenceTable[{a[0]==a[1]==a[2]==a[3]==a[4]==a[5]==a[6]==a[7]==1, a[8]==1, a[n]==(a[n-1]a[n-4]+a[n-5]a[n-8])/a[n-9]}, a, {n, 30}] (* Harvey P. Dale, Mar 18 2018 *)
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PROG
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(PARI) {a(n) = if( n<0, n = 8-n); if( n<9, 1, (a(n-1)*a(n-4) + a(n-5)*a(n-8)) / a(n-9))};
(Magma) I:=[1, 1, 1, 1, 1, 1, 1, 1, 1]; [n le 9 select I[n] else (Self(n-1)*Self(n-4) + Self(n-5)*Self(n-8))/Self(n-9): n in [1..30]]; // G. C. Greubel, Aug 10 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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