A036995 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.

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, 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, 16, 22, 11, 1, 7, 7, 8, 8, 12, 7, 18, 15, 19, 26, 12

Offset

0,3

Comments

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

Links

Table of n, a(n) for n=0..77.

S. Dulucq, Etude combinatoire de problèmes d'énumération, d'algorithmique sur les arbres et de codage par des mots, a thesis presented to l'Université de Bordeaux I, 1987. (Annotated scanned copy)

S. Dulucq and D. Gouyou-Beauchamps, Sur les facteurs des suites de Sturm, Theoret. Comput. Sci. 71 (1990), 381-400.

Formula

Th. 6.2 of the reference gives a generating function.

Crossrefs

Sequence in context: A075106 A196935 A226314 * A225597 A116908 A265146

Adjacent sequences: A036992 A036993 A036994 * A036996 A036997 A036998

Keyword

nonn,easy,tabl

Author

N. J. A. Sloane

Extensions

More terms from Dulucq and Gouyou-Beauchamps added by Sean A. Irvine, Dec 04 2020

Status

approved