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%I #23 May 06 2024 01:45:02
%S 41,1613,9080,29462,72479,150551,278798,475040,759797,1156289,1690436,
%T 2390858,3288875,4418507,5816474,7522196,9577793,12028085,14920592,
%U 18305534,22235831,26767103,31957670
%N The maximum number of points obtainable in a game of Entanglement on a board of radius n.
%C The standard board has a radius of 3 and a maximum score of a(3) = 9080.
%H Harvey P. Dale, <a href="/A180667/b180667.txt">Table of n, a(n) for n = 1..1000</a>
%H GopherWood Studios, <a href="http://entanglement.gopherwoodstudios.com">Entanglement</a>
%H Nathaniel Johnston, <a href="http://www.nathanieljohnston.com/2011/01/the-maximum-score-in-the-game-entanglement-is-9080/">The Maximum Score in the Game "Entanglement" is 9080</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F a(n) = (225/2)*n^4 + 45*n^3 - 135*n^2 - (51/2)*n + 44.
%F a(n) = +5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+ a(n-5).
%F G.f.: -x*(41+1408*x+1425*x^2-218*x^3+44*x^4)/(x-1)^5.
%t LinearRecurrence[{5,-10,10,-5,1},{41,1613,9080,29462,72479},30] (* _Harvey P. Dale_, Jul 04 2019 *)
%K nonn,easy
%O 1,1
%A _Nathaniel Johnston_, Jan 21 2011