%I A060853
%S A060853 1,20,210,1540,8855,42504,177100,657800,2220075,6906900,20030010,
%T A060853 54627084,141116637,347336412,818558424,1854631380,4053948342,
%U A060853 8574134256,17590903116,35084425512,68153183370,129156542039
%N A060853 Number of possible games of 10-pin bowling with a total score of n.
%C A060853 For small n, this is equal to the binomial coefficient C(n,19). We have 
               eleven possibilities for the first ball thrown in the first frame 
               (gutter, 1, 2, ..., 9, strike) and the same possibilities occur for 
               each of the other nine frames. So without even considering the second 
               ball in each frame, at a minimum we have 11^10 possibilities. In 
               fact, the true number of games is much larger due to the effect of 
               the second ball in each frame. It's easy to show that the total number 
               of possible games is: 66^9 * 241 = 5726805883325784576. The number 
               of possible games with scores n = 0, 1, 2, 3, 4, 5, are: 1, 20, 210, 
               1540, 8855, 42504... The maximal number of possible games is for 
               the score n = 77, namely 172542309343731946. Then there are a declining 
               number of ways to get very high scores. For n = 288, 289, ..., 300 
               the totals are: 12, 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1. The distribution 
               of number of possible games as a function of n is not precisely symmetric 
               about its maximal point. - Jonathan Vos Post (jvospost3(AT)gmail.com), 
               Jul 15 2005
%D A060853 Cooper, C. N. and Kennedy, R. E. "A Generating Function for the Distribution 
               of the Scores of All Possible Bowling Games." In The Lighter Side 
               of Mathematics (Ed. R. K. Guy and R. E. Woodrow). Washington, DC: 
               Math. Assoc. Amer., 1994.
%D A060853 Cooper, C. N. and Kennedy, R. E. "Is the Mean Bowling Score Awful?" In 
               The Lighter Side of Mathematics (Ed. R. K. Guy and R. E. Woodrow). 
               Washington, DC: Math. Assoc. Amer., 1994.
%D A060853 Curtis Cooper and Robert E. Kennedy, Mathematics Magazine, Vol. 63, No. 
               4, pp. 239-243. (Year?)
%H A060853 Lee A. Newberg, <a href="b060853.txt">Table of n, a(n) for n=0..300</
               a>
%H A060853 Balmoral Software, <a href="http://www.balmoralsoftware.com/bowling/bowling.htm">
               All About Bowling Scores</a>, 2005,
%H A060853 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Bowling.html">Bowling</a>.
%e A060853 The final terms are a(290) = 11, a(291) = ... = a(300) = 1.
%Y A060853 Cf. A010972.
%Y A060853 Sequence in context: A074668 A139620 A094311 this_sequence A010972 A126905 
               A022585
%Y A060853 Adjacent sequences: A060850 A060851 A060852 this_sequence A060854 A060855 
               A060856
%K A060853 nonn,fini,easy
%O A060853 0,2
%A A060853 Micah Friese (friesem(AT)stolaf.edu), May 03 2001
%E A060853 n = 77 peak value corrected by Lee A. Newberg (integer(AT)quantconsulting.com), 
               Oct 30 2009