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A190783 a(n) = (a(n-1)*a(n-4) + a(n-5)*a(n-8)) / a(n-9), a(0) = ... = a(8) = 1. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,10

COMMENTS

The recursion exhibits the Laurent phenomenon.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..36

Sergey Fomin and Andrei Zelevinsky, The Laurent phenomenon, arXiv:math/0104241v1 [math.CO] (2001).

Sergey Fomin and Andrei Zelevinsky, The Laurent phenomenon, Advances in Applied Mathematics 28 (2002), 119-144.

FORMULA

A078918(n) = a(n+4)*a(n+2)*a(n+1)*a(n-1).

a(8-n) = a(n).

MATHEMATICA

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 *)

PROG

(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

CROSSREFS

Cf. A078918.

Sequence in context: A217650 A032988 A280206 * A136367 A014545 A158930

Adjacent sequences:  A190780 A190781 A190782 * A190784 A190785 A190786

KEYWORD

nonn

AUTHOR

Michael Somos, Dec 29 2012

STATUS

approved

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Last modified June 28 17:19 EDT 2022. Contains 354907 sequences. (Running on oeis4.)