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A051786
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Propp's cubic recurrence: a(0) = a(1) = a(2) = a(3) = 1; a(n)=(1+a(n-1)*a(n-2)*a(n-3))/a(n-4).
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3
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1, 1, 1, 1, 2, 3, 7, 43, 452, 45351, 125920291, 60027819184831, 758397193749171922281611, 126403219004744354228963383975713263866432, 45699526286117471520994956894648733172150425791690122432447239675853643
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OFFSET
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0,5
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REFERENCES
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Jim Propp (propp(AT)math.wisc.edu), personal communication.
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LINKS
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Table of n, a(n) for n=0..14.
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FORMULA
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a(-n) = a(n + 3). a(0) = a(1) = a(2) = a(3) = 1. a(n + 2) * a(n - 2) = 1 + a(n + 1) * a(n) * a(n - 1).
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MATHEMATICA
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RecurrenceTable[{a[1]==a[2]==a[3]==a[4]==1, a[n]==(1+a[n-1]a[n-2]a[n-3])/ a[n-4]}, a[n], {n, 15}] (* From Harvey P. Dale, May 14 2011 *)
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PROG
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(PARI) {a(n) = if( n<0, n = 3-n); if( n<4, 1, (a(n-1) * a(n-2) * a(n-3) + 1) / a(n-4)) } /* Michael Somos, Oct 16 2006 */
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CROSSREFS
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Cf. A005246.
Sequence in context: A000946 A091771 A072714 * A133400 A113845 A072713
Adjacent sequences: A051783 A051784 A051785 * A051787 A051788 A051789
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KEYWORD
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nonn,nice,easy
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AUTHOR
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Michael Somos, Dec 09 1999
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EXTENSIONS
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Edited by N. J. A. Sloane at the suggestion of Andrew Plewe, Jun 17 2007
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STATUS
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approved
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