A284838 Number of edges in the n-Keller graph.

0, 40, 1088, 21888, 397312, 6883328, 116244480, 1932230656, 31778668544, 518791888896, 8424565768192, 136279337467904, 2198302774788096, 35386835907641344, 568757233463066624, 9130929873047519232, 146464646890277306368, 2347871574175904694272

Offset

1,2

Links

Colin Barker, Table of n, a(n) for n = 1..800

Eric Weisstein's World of Mathematics, Keller Graph

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

Formula

a(n) = 2^(2*n-1)*(4^n-3^n-n).

From Robert Israel, Apr 04 2017: (Start)

G.f.: 8*(5-44*x)*x^2/((1-16*x)*(1-12*x)*(1-4*x)^2).

E.g.f.: exp(16*x)/2-exp(12*x)/2-2*x*exp(4*x).

(End)

a(n) = 36*a(n-1) - 432*a(n-2) + 1984*a(n-3) - 3072*a(n-4) for n>4. - Colin Barker, Apr 04 2017

Maple

f:= n -> 2^(2*n-1)*(4^n-3^n-n):
map(f, [$1..30]); # Robert Israel, Apr 04 2017

Mathematica

Table[2^(2 n - 1) (4^n - 3^n - n), {n, 15}]
LinearRecurrence[{36, -432, 1984, -3072}, {0, 40, 1088, 21888}, 20] (* Eric W. Weisstein, Mar 21 2018 *)
CoefficientList[Series[-((8 x (-5 + 44 x))/((1 - 4 x)^2 (1 - 28 x + 192 x^2))), {x, 0, 20}], x] (* Eric W. Weisstein, Mar 21 2018 *)

Prog

(PARI) concat(0, Vec(8*(5-44*x)*x^2/((1-16*x)*(1-12*x)*(1-4*x)^2) + O(x^30))) \\ Colin Barker, Apr 04 2017
(Python) def a(n): return 2**(2*n-1)*(4**n-3**n-n) # Indranil Ghosh, Apr 04 2017

Crossrefs

Cf. A000302(n) = 4^n (number of vertices in the n-Keller graph).

Cf. A284850(n) = a(n)/2^(2*n-1) (vertex degrees of the n-Keller graph).

Sequence in context: A165380 A075907 A062143 * A124100 A071952 A331906

Adjacent sequences: A284835 A284836 A284837 * A284839 A284840 A284841

Keyword

nonn,easy

Author

Eric W. Weisstein, Apr 03 2017

Status

approved