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
KEYWORD
nonn
AUTHOR
Michael Somos, Dec 29 2012
STATUS
approved