

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
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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*(1x^20)/(1x)+x^2*(1x^40)/(1x^2)+x^3*(1x^60)/(1x^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 (1x^20)/(1x)+x^2(1x^40)/(1x^2)+ x^3(1 x^60)/ (1x^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



