A180667 The maximum number of points obtainable in a game of Entanglement on a board of radius n.

41, 1613, 9080, 29462, 72479, 150551, 278798, 475040, 759797, 1156289, 1690436, 2390858, 3288875, 4418507, 5816474, 7522196, 9577793, 12028085, 14920592, 18305534, 22235831, 26767103, 31957670

Offset

1,1

Comments

The standard board has a radius of 3 and a maximum score of a(3) = 9080.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1)

GopherWood Studios, Entanglement

N. Johnston, The Maximum Score in the Game "Entanglement" is 9080

Formula

a(n) = (225/2)*n^4 + 45*n^3 - 135*n^2 - (51/2)*n + 44.

a(n) = +5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+ a(n-5).

G.f.: -x*(41+1408*x+1425*x^2-218*x^3+44*x^4)/(x-1)^5.

Mathematica

LinearRecurrence[{5, -10, 10, -5, 1}, {41, 1613, 9080, 29462, 72479}, 30] (* Harvey P. Dale, Jul 04 2019 *)

Crossrefs

Sequence in context: A076462 A163050 A305863 * A281608 A162878 A163224

Adjacent sequences: A180664 A180665 A180666 * A180668 A180669 A180670

Keyword

nonn,easy

Author

Nathaniel Johnston, Jan 21 2011

Status

approved