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
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Dec 07 2017
EXTENSIONS
Terms a(8) and beyond from Andrew Howroyd, Dec 09 2017
STATUS
approved