A060309 A001067 appears to count the periodic points for a certain map. If so, then this is the sequence of the numbers of orbits of length n.

1, 0, 0, 0, 0, 115, 0, 452, 4874, 17461, 7062, 19696950, 50610, 242341439, 114877883680, 481832564850, 8919335150, 1461959530725195586, 8116326631140, 13054135924822447372, 72385602091336704890, 115013510658268698717, 1127506827209663824722

Offset

1,6

Links

Table of n, a(n) for n=1..23.

Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.

T. Ward, Exactly realizable sequences

Formula

If b(n) is the n-th term of A001067, then a(n)=(1/n)* |Sum_{d|n}mu(d)b(n/d)|, n<>2.

Example

a(11) = 7062 because the 11th term of A001067 is 77683 and the first term is 1, so there should be (77683-1)/11 = 7062 orbits of length 11.

Crossrefs

Cf. A001067, A060171, A060479.

Sequence in context: A230463 A200807 A084877 * A101111 A129823 A056035

Adjacent sequences: A060306 A060307 A060308 * A060310 A060311 A060312

Keyword

nonn

Author

Thomas Ward, Apr 10 2001

Extensions

a(18) corrected and more terms from Sean A. Irvine, Nov 08 2022

Status

approved