A167213 - OEIS

%I #11 Jun 05 2016 23:49:21

%S 1,1,3,7,17,40,98,233,562,1349,3243,7789,18722,44978,108083,259700,

%T 624027,1499427,3602913,8657216,20801982,49983920,120103675,288590527,

%U 693438537,1666225599,4003682857,9620231375,23115930197,55544009564

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

%C 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.

%H G. C. Greubel, <a href="/A167213/b167213.txt">Table of n, a(n) for n = 0..1000</a>

%F 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)).

%e 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".

%t 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 *)

%K easy,nonn

%O 0,3

%A _Lee A. Newberg_, Oct 30 2009