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

0,3

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.

Links

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

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)).

Example

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".

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 *)

Crossrefs

Sequence in context: A247300 A137682 A190360 * A249753 A000600 A138901

Adjacent sequences: A167210 A167211 A167212 * A167214 A167215 A167216

Keyword

easy,nonn

Author

Lee A. Newberg, Oct 30 2009

Status

approved