OFFSET
1,7
COMMENTS
Any six successive terms satisfy the Markoff-Hurwitz equation a^2 + b^2 + c^2 + d^2 + e^2 + f^2 = 6*a*b*c*d*e*f. - Bruno Langlois, Aug 09 2016
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..17
Andrew N. W. Hone, Diophantine non-integrability of a third order recurrence with the Laurent property, arXiv:math/0601324 [math.NT], 2006.
Andrew N. W. Hone, Diophantine non-integrability of a third order recurrence with the Laurent property, J. Phys. A: Math. Gen. 39 (2006), L171-L177.
Matthew Christopher Russell, Using experimental mathematics to conjecture and prove theorems in the theory of partitions and commutative and non-commutative recurrences, PhD Dissertation, Mathematics Department, Rutgers University, May 2016.
FORMULA
a(n) = 6*a(n-1)*a(n-2)*a(n-3)*a(n-4)*a(n-5) - a(n-6). - Bruno Langlois, Aug 09 2016
MATHEMATICA
RecurrenceTable[{a[n] == (a[n - 1]^2 + a[n - 2]^2 + a[n - 3]^2 + a[n - 4]^2 + a[n - 5]^2)/a[n - 6], a[1] == a[2] == a[3] == a[4] == a[5] == a[6] == 1}, a, {n, 1, 14}] (* Michael De Vlieger, Aug 11 2016 *)
nxt[{a_, b_, c_, d_, e_, f_}] := {b, c, d, e, f, (b^2+c^2+d^2+e^2+f^2)/a}; NestList[ nxt, Table[1, 6], 20][[All, 1]] (* Harvey P. Dale, Mar 18 2018 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, Jul 28 2002
STATUS
approved