A284850 a(n) = 4^n - 3^n - n.

0, 5, 34, 171, 776, 3361, 14190, 58967, 242452, 989517, 4017146, 16245763, 65514528, 263652473, 1059392902, 4251920559, 17050729004, 68332056229, 273715645458, 1096024843355, 4387586157880, 17560804984785, 70274600998814, 281192547174151, 1125052618233156

Offset

1,2

Comments

Vertex degree, edge chromatic number, edge connectivity, and spectral radius of the n-Keller graph.

Links

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

Witold Jarnicki, W. Myrvold, P. Saltzman, S. Wagon, Properties, Proved and Conjectured, of Keller, Mycielski, and Queen Graphs, arXiv preprint arXiv:1606.07918 [math.CO], 2016.

Eric Weisstein's World of Mathematics, Keller Graph

Eric Weisstein's World of Mathematics, Spectral Radius

Index entries for linear recurrences with constant coefficients, signature (9,-27,31,-12).

Formula

From Colin Barker, Apr 04 2017: (Start)

G.f.: x^2*(5 - 11*x) / ((1 - x)^2*(1 - 3*x)*(1 - 4*x)).

a(n) = 9*a(n-1) - 27*a(n-2) + 31*a(n-3) - 12*a(n-4) for n>4.

(End)

E.g.f.: exp(4*x) - exp(3*x) - x*exp(x). - Indranil Ghosh, Apr 04 2017

Mathematica

Table[(4^n - 3^n - n), {n, 30}]
CoefficientList[ Series[(5x - 11x^2)/((x - 1)^2 (1 - 7x + 12x^2)), {x, 0, 25}], x] (* or *)
LinearRecurrence[{9, -27, 31, -12}, {0, 5, 34, 171}, 26] (* Robert G. Wilson v, Mar 08 2018 *)

Prog

(PARI) concat(0, Vec(x^2*(5 - 11*x) / ((1 - x)^2*(1 - 3*x)*(1 - 4*x)) + O(x^30))) \\ Colin Barker, Apr 04 2017
(Python) def a(n): return 4**n - 3**n - n # Indranil Ghosh, Apr 04 2017

Crossrefs

Cf. A284838(n) = 2^(2*n-1)*a(n) (edge count in n-Keller graph).

Sequence in context: A034224 A167023 A316559 * A248373 A121831 A076708

Adjacent sequences: A284847 A284848 A284849 * A284851 A284852 A284853

Keyword

nonn,easy

Author

Eric W. Weisstein, Apr 04 2017

Status

approved