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
GopherWood Studios, Entanglement
Nathaniel Johnston, The Maximum Score in the Game "Entanglement" is 9080
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
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
KEYWORD
nonn,easy
AUTHOR
Nathaniel Johnston, Jan 21 2011
STATUS
approved