A185278 Number of isomorphism classes of generalized Petersen graphs G(n,k) on 2n vertices with gcd(n,k) = 1.

1, 1, 2, 1, 2, 2, 2, 2, 3, 2, 4, 2, 3, 3, 5, 2, 5, 3, 4, 3, 6, 4, 6, 4, 5, 4, 8, 3, 8, 5, 6, 5, 7, 4, 10, 5, 7, 6, 11, 4, 11, 6, 7, 6, 12, 6, 11, 6, 9, 7, 14, 5, 11, 8, 10, 8, 15, 6, 16, 8, 10, 9, 14, 6, 17, 9, 12, 7, 18, 8, 19, 10, 11, 10, 16, 7, 20, 10, 14, 11, 21, 8, 18, 11, 15, 12, 23, 7, 19, 12, 16, 12, 19, 10, 25, 11, 16, 11

Offset: 3

Author

N. J. A. Sloane, Feb 19 2011

Keywords

• nonn
• look

Links

• Robert Israel, Table of n, a(n) for n = 3..10000
• Marko Petkovsek and Helena Zakrajsek, Enumeration of I-graphs: Burnside does it again, Ars Mathematica Contemporanea, 2 (2009) 241-262.
• A. Steimle and W. Staton, The isomorphism classes of the generalized Petersen graphs, Discrete Math. 309 (2009), 231-237.

Crossrefs

Cf. A000010, A000089, A060594.

Programs

Maple

# using functions A060594 and A000089 as defined in those sequences
f:= n -> (numtheory:-phi(n)+A060594(n)+A000089(n))/4:
map(f, [$3..100]); # Robert Israel, Sep 06 2018

Formula

a(n) = (A000010(n) + A060594(n) + A000089(n))/4.