%I A036692
%S A036692 1,2,14,84,556,3736,25612,177688,1244398,8777612,62271384,443847648,
%T A036692 3175924636,22799963576,164142004184,1184574592592,8567000931404,
%U A036692 62073936511496,450518481039956,3274628801768744,23833760489660324
%N A036692 T(2n,n) with T as in A036355.
%H A036692 Moa APAGODU and Doron ZEILBERGER, <a href="http://www.math.rutgers.edu/
               ~zeilberg/mamarim/mamarimhtml/appswz.html">FIVE Applications of Wilf-Zeilberger 
               Theory to Enumeration and Probability</a>
%F A036692 Comment from N. J. A. Sloane, Jul 14 2009: The following remarks and 
               formulas are basically copied from the Apagodu-Zeilberger reference, 
               where this sequence appears as an example. (Start)
%F A036692 These are the (old-time) basketball numbers, giving the number of ways 
               a basketball game that ended with the score n : n can proceed. Recall 
               that in the old days (before 1961), an atom of basketball-scoring 
               could be only of one or two points.
%F A036692 Equivalently, this number is the number of ways of walking, in the square 
               lattice, from (0; 0) to (n; n) using the atomic steps {(1; 0); (2; 
               0); (0; 1); (0; 2)}.
%F A036692 It satisfies the third-order linear recurrence:
%F A036692 (16/5)(2n + 3)(11n + 26)(1 + n)/((n + 3)(2 + n)(11n + 15))a(n)
%F A036692 -(4/5)(121n^3 + 649n^2 + 1135n + 646)/((n + 3)(2 + n)(11n + 15))a(1 + 
               n)
%F A036692 -(2/5)(176n^2 + 680n + 605)/((11n + 15)(n + 3))a(2 + n) + a(n + 3) = 
               0 ;
%F A036692 subject to the initial conditions: a(0) = 1; a(1) = 2; a(2) = 14 :
%F A036692 Asymptotics (moused from pdf file, should be checked!): (.37305616)(4 
               + 2*sqrt(3))^n*n^(-1/2)(1 + (67/1452)*sqrt(3)-(119/484))/n +((6253/
               117128)-(7163/234256)sqrt(3))/n^2+(-(32645/15460896)sqrt(3)+(129625/
               10307264))/n^3). (End)
%Y A036692 Sequence in context: A077444 A138126 A053141 this_sequence A075140 A037563 
               A005610
%Y A036692 Adjacent sequences: A036689 A036690 A036691 this_sequence A036693 A036694 
               A036695
%K A036692 nonn
%O A036692 0,2
%A A036692 Floor van Lamoen (fvlamoen(AT)hotmail.com)
%E A036692 Extended by Christian G. Bower (bowerc(AT)usa.net), Nov 18 2003