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A301571
Number of vertices at distance 2 from a given vertex in the n-Keller graph.
1
0, 10, 29, 84, 247, 734, 2193, 6568, 19691, 59058, 177157, 531452, 1594335, 4782982, 14348921, 43046736, 129140179, 387420506, 1162261485, 3486784420, 10460353223, 31381059630, 94143178849, 282429536504, 847288609467, 2541865828354, 7625597485013
OFFSET
1,2
COMMENTS
The radius of the n-Keller graph is 2 for n > 1. - Andrew Howroyd, Mar 23 2018
LINKS
Eric Weisstein's World of Mathematics, Graph Distance
Eric Weisstein's World of Mathematics, Keller Graph
FORMULA
a(n) = 3^n + n - 1 for n > 1. - Andrew Howroyd, Mar 23 2018
From Colin Barker, Mar 24 2018: (Start)
G.f.: x^2*(5 - 3*x)*(2 - 3*x) / ((1 - x)^2*(1 - 3*x)).
a(n) = 5*a(n-1) - 7*a(n-2) + 3*a(n-3) for n>4.
(End)
PROG
(PARI) concat(0, Vec(x^2*(5 - 3*x)*(2 - 3*x) / ((1 - x)^2*(1 - 3*x)) + O(x^60))) \\ Colin Barker, Mar 24 2018
CROSSREFS
Cf. A284850 (number of vertices at distance 1 = vertex degree), A292056.
Sequence in context: A200185 A372710 A321140 * A027979 A181102 A057456
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Mar 23 2018
STATUS
approved