

A072879


a(n) = 5*a(n1)*a(n2)*a(n3)*a(n4)  a(n5) with a(1) = a(2) = a(3) = a(4) = a(5) = 1.


12



1, 1, 1, 1, 1, 4, 19, 379, 144019, 20741616379, 107553662508585672001, 608831069421618273050865038881215685876, 978035016076705458999330010986670207956236476587064788804921180339451725001
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OFFSET

1,6


COMMENTS

Solutions of the Hurwitz equation in five variables.


LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..16
Arthur Baragar, Integral solutions of the MarkoffHurwitz equations, J. Number Theory 49 (1994), 2744.
Andrew N. W. Hone, Diophantine nonintegrability of a third order recurrence with the Laurent property, arXiv:math/0601324 [math.NT], 2006.
Andrew N. W. Hone, Diophantine nonintegrability of a third order recurrence with the Laurent property, J. Phys. A: Math. Gen. 39 (2006), L171L177.
Matthew Christopher Russell, Using experimental mathematics to conjecture and prove theorems in the theory of partitions and commutative and noncommutative recurrences, PhD Dissertation, Mathematics Department, Rutgers University, May 2016.


FORMULA

a(1) = a(2) = a(3) = a(4) = a(5) = 1; a(n) = (a(n1)^2+a(n2)^2+a(n3)^2+a(n4)^2)/a(n5) for n >= 6.
From the recurrence a(n) = 5*a(n1)*a(n2)*a(n3)*a(n4)  a(n5), any five successive terms satisfy the fivevariable Hurwitz equation a(n)^2+a(n1)^2+a(n2)^2+a(n3)^2+a(n4)^2 = 5*a(n)*a(n1)*a(n2)*a(n3)*a(n4). As n tends to infinity, the limit of log(log(a(n)))/n is log x = 0.6562559790..., where x=1.927561975... is the largest real root of the quartic x^4x^3x^2x1=0.  Andrew Hone, Nov 16 2005


MATHEMATICA

nxt[{a_, b_, c_, d_, e_}]:={b, c, d, e, (5b c d e)a}; NestList[nxt, {1, 1, 1, 1, 1}, 20][[All, 1]] (* Harvey P. Dale, Nov 07 2016 *)


CROSSREFS

Cf. A006720, A064098, A072878, A072880.
Sequence in context: A126147 A007411 A276259 * A112958 A080991 A000844
Adjacent sequences: A072876 A072877 A072878 * A072880 A072881 A072882


KEYWORD

easy,nonn


AUTHOR

Benoit Cloitre, Jul 28 2002


EXTENSIONS

Entry revised Nov 19 2005, based on comments from Andrew Hone
Name clarified by Petros Hadjicostas, May 11 2019


STATUS

approved



