A167213 The number of ordered ways to achieve a score of n in darts.

1, 1, 3, 7, 17, 40, 98, 233, 562, 1349, 3243, 7789, 18722, 44978, 108083, 259700, 624027, 1499427, 3602913, 8657216, 20801982, 49983920, 120103675, 288590527, 693438537, 1666225599, 4003682857, 9620231375, 23115930197, 55544009564

Offset: 0

Author

Lee A. Newberg, Oct 30 2009

Keywords

• easy
• nonn

Comments

The game of darts has unmodified scores (1, 2, ..., 20), doubles of those values (2, 4, ..., 40), triples of those values (3, 6, ..., 60), and bull's eye values of 25 and 50.

Examples

			There are 7 ordered ways to get a total score of 3: (#1) "1","1","1"; (#2) "2","1"; (#3) "1","2"; (#4) "double 1","1" (#5) "1","double 1"; (#6) "triple 1"; and (#7) "3".
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Programs

Mathematica

CoefficientList[Series[1/(1-(x (1-x^20)/(1-x)+x^2(1-x^40)/(1-x^2)+ x^3(1- x^60)/ (1-x^3)+x^25+x^50)),{x,0,30}],x] (* Harvey P. Dale, Jul 04 2011 *)

Formula

G.f. = 1/(1-(x*(1-x^20)/(1-x)+x^2*(1-x^40)/(1-x^2)+x^3*(1-x^60)/(1-x^3)+x^25+x^50)).