A301571 Number of vertices at distance 2 from a given vertex in the n-Keller graph.

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

Colin Barker, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Graph Distance

Eric Weisstein's World of Mathematics, Keller Graph

Index entries for linear recurrences with constant coefficients, signature (5,-7,3).

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: A055850 A200185 A321140 * A027979 A181102 A057456

Adjacent sequences: A301568 A301569 A301570 * A301572 A301573 A301574

Keyword

nonn,easy

Author

Eric W. Weisstein, Mar 23 2018

Status

approved