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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. 0
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 (list; table; graph; refs; listen; history; text; internal format)
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..45.

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,more

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified July 9 14:41 EDT 2020. Contains 335543 sequences. (Running on oeis4.)