|
%I #19 Dec 05 2020 12:04:13
%S 1,1,2,1,2,3,1,3,3,4,1,3,3,5,5,1,4,4,4,7,6,1,4,5,4,7,9,7,1,5,4,7,5,9,
%T 12,8,1,5,6,6,5,10,10,15,9,1,6,6,7,9,6,12,13,18,10,1,6,6,7,11,6,13,12,
%U 16,22,11,1,7,7,8,8,12,7,18,15,19,26,12
%N Triangle of numbers a(i,j), i+j = n >= 2, giving number of words in a certain language with i 0's, j 1's, ending with 1.
%C Generating function f(x,y) = g(x,y) + Sum_{m>=1} x*y*(1-y^m) *( f(x*y^m,x*y^(m+1)) +f(x*y^(m+1),x*y^m) )/(1-y) + Sum_{m>=0} y*( f(y*x^m,y*x^(m+1)) +f(y*x^(m+1),y*x^m) ) + Sum_{m>=0} f(x*y^m,x*y^(m+1)), where g(x,y) = y*(x*y)/(1-x*y) + Sum_{m>=1} ( x*y^m*x*y^(m+1)/(1-x*y^(m+1)) + x*y^m/(1-x*y^m) ) + Sum_{m>=1} (y*y*x^(m+1)/(1-y*x^(m+1)) + x*y*x*y^(m+2)*(1-y^m)/(1-y)/(1-x*y^(m+2)) ). - _R. J. Mathar_, Sep 30 2011
%H S. Dulucq, <a href="/A005819/a005819.pdf">Etude combinatoire de problèmes d'énumération, d'algorithmique sur les arbres et de codage par des mots</a>, a thesis presented to l'Université de Bordeaux I, 1987. (Annotated scanned copy)
%H S. Dulucq and D. Gouyou-Beauchamps, <a href="http://dx.doi.org/10.1016/0304-3975(90)90050-R">Sur les facteurs des suites de Sturm</a>, Theoret. Comput. Sci. 71 (1990), 381-400.
%F Th. 6.2 of the reference gives a generating function.
%K nonn,easy,tabl
%O 0,3
%A _N. J. A. Sloane_
%E More terms from Dulucq and Gouyou-Beauchamps added by _Sean A. Irvine_, Dec 04 2020
|
