A296189 Harary index for the n-Keller graph.

0, 80, 1552, 27264, 460544, 7634944, 125227008, 2039840768, 33069137920, 534273589248, 8610328346624, 138508408717312, 2225051277459456, 35707816396193792, 572608992614809600, 9177150953877405696, 147019299735681892352, 2354527407788183781376

Offset

1,2

Comments

The n-Keller graph is distance regular with 4^n vertices and for n > 1 the radius is 2. The degree of each vertex is 4^n - 3^n - n. - Andrew Howroyd, Dec 09 2017

Links

Andrew Howroyd, Table of n, a(n) for n = 1..100

Eric Weisstein's World of Mathematics, Harary Index

Eric Weisstein's World of Mathematics, Keller Graph

Index entries for linear recurrences with constant coefficients, signature (36, -432, 1984, -3072).

Formula

a(n) = 4^n*(4^n - (3^n + n + 1)/2)/2 for n > 1. - Andrew Howroyd, Dec 09 2017

a(n) = 36*a(n-1) - 432*a(n-2) + 1984*a(n-3) - 3072*a(n-4) for n > 5. - Eric W. Weisstein, Dec 09 2017

G.f.: -(16*x^2 (-5 + 83*x - 372*x^2 + 576*x^3)/((-1 + 4*x)^2*(1 - 28*x + 192*x^2))). - Eric W. Weisstein, Dec 09 2017

Mathematica

Table[If[n == 1, 0, 4^(n - 1) (2^(2 n + 1) - 3^n - n - 1)], {n, 20}]
Join[{0}, LinearRecurrence[{36, -432, 1984, -3072}, {80, 1552, 27264, 460544}, 20]]
CoefficientList[Series[-(16 x (-5 + 83 x - 372 x^2 + 576 x^3)/((-1 + 4 x)^2 (1 - 28 x + 192 x^2))), {x, 0, 20}], x]

Prog

(PARI) a(n) = if(n>1, 4^n*(4^n - (3^n+n+1)/2)/2); \\ Andrew Howroyd, Dec 09 2017

Crossrefs

Cf. A292056.

Sequence in context: A199533 A333075 A323962 * A060623 A173782 A332580

Adjacent sequences: A296186 A296187 A296188 * A296190 A296191 A296192

Keyword

nonn

Author

Eric W. Weisstein, Dec 07 2017

Extensions

Terms a(8) and beyond from Andrew Howroyd, Dec 09 2017

Status

approved