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A180667 The maximum number of points obtainable in a game of Entanglement on a board of radius n. 1
41, 1613, 9080, 29462, 72479, 150551, 278798, 475040, 759797, 1156289, 1690436, 2390858, 3288875, 4418507, 5816474, 7522196, 9577793, 12028085, 14920592, 18305534, 22235831, 26767103, 31957670 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 8 17:01 EST 2021. Contains 349596 sequences. (Running on oeis4.)