OFFSET
0,3
COMMENTS
a(k) is the optimal competitive ratio of any memoryless algorithm for the weighted k-server problem (Chiplunkar and Vishwanathan). - David Eppstein, Dec 31 2013
This is a divisibility sequence, that is if n divides m then a(n) divides a(m). Cf. A002065. - Peter Bala, Mar 26 2018
LINKS
Harry J. Smith, Table of n, a(n) for n = 0..12
Ashish Chiplunkar and Sundar Vishwanathan, On Randomized Memoryless Algorithms for the Weighted k-server Problem, 54th IEEE Symp. Foundations of Computer Science (FOCS 2013), pp. 11-19; arXiv:1301.0123
FORMULA
EXAMPLE
a(3) = a(2)^2 + 3*a(2) + 1 = 25 + 15 + 1 = 41.
PROG
(PARI) a(n)=if(n<1, 0, a(n-1)^2+3*a(n-1)+1);
(PARI) { for (n=0, 12, a=if(n, a^2 + 3*a + 1, 0); write("b065035.txt", n, " ", a) ) } \\ Harry J. Smith, Oct 03 2009
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Henry Bottomley, Nov 03 2001
STATUS
approved