A060202 Let G = complete graph on 4 vertices, create the sequence G, L(G), L(L(G)), L(L(L(G))), ... where each graph in this sequence is the line graph of the previous graph; a(n) is number of vertices of the n-th graph in this sequence.

4, 6, 12, 36, 180, 1620, 27540, 908820, 59073300, 7620455700, 1958457114900, 1004688499943700, 1029805712442292500, 2110071904794257332500, 8644964593942072291252500, 70828194918167398282231732500

Offset: 0

Author

Avi Peretz (njk(AT)netvision.net.il), Mar 18 2001

Keywords

• nonn

Comments

If G is k-regular, then L(G) is (2k-2)-regular. From this it is easy to get the formula for a(n).

Examples

			The line graph of the complete graph on 4 vertices has C(4,2) vertices so a(1) = 6.
		

Programs

Maple

for n from 0 to 30 do printf(`%d,`,4*product(1+2^(k-2), k=1..n)) od:

Formula

a(0)=4 and for n >= 1 a(n) = 4 * product k=1...n (1+2^(k-2))

Extensions

More terms from James Sellers and Vladeta Jovovic, Mar 26 2001