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A036995
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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.
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0
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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
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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COMMENTS
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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
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LINKS
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FORMULA
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Th. 6.2 of the reference gives a generating function.
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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More terms from Dulucq and Gouyou-Beauchamps added by Sean A. Irvine, Dec 04 2020
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STATUS
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approved
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