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 A167213 The number of ordered ways to achieve a score of n in darts. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified April 3 15:51 EDT 2020. Contains 333197 sequences. (Running on oeis4.)