Search: id:A060173 Results 1-1 of 1 results found. %I A060173 %S A060173 1,1,1,2,1,6,1,12,10,30,1,139,1,252,231,920,1,3780,1,10250,5601,32076, %T A060173 1,149390,2126,400036,173692,1475642,1,6196651,1,19113136,5864915, %U A060173 68635494,201405,289525026,1 %N A060173 Number of orbits of length n under a map whose periodic points are counted by A056045. %C A060173 The sequence A056045 records the number of points of period n under a map. The number of orbits of length n for this map gives the sequence above. %D A060173 Yash Puri and Thomas Ward, A dynamical property unique to the Lucas sequence, Fibonacci Quarterly, Volume 39, Number 5 (November 2001), pp. 398-402. %H A060173 Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1. %F A060173 If a(n) is the n-th term of A056045, then the n-th term is u(n) = (1/ n)* Sum_{ d divides n }\mu(d)a(n/d) %e A060173 u(7) = 1 since the map whose periodic points are counted by A056045 has 1 fixed point and 8 points of period 7, hence 1 orbits of length 7. %Y A060173 Cf. A056045, A060164, A060165, A060166, A060167, A060168, A060169, A060170, A060171, A060172. %Y A060173 Sequence in context: A107754 A139625 A053785 this_sequence A059344 A109193 A083720 %Y A060173 Adjacent sequences: A060170 A060171 A060172 this_sequence A060174 A060175 A060176 %K A060173 easy,nonn %O A060173 1,4 %A A060173 Thomas Ward (t.ward(AT)uea.ac.uk), Mar 13 2001 Search completed in 0.001 seconds