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Search: id:A121946
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| A121946 |
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Let r be the matrix {{1,1},{0,1}} and b={{1,0},{1,0}}. Let A be the semigroup generated by r and b. a(n) is the number of words of length n in A. |
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+0
1
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| 1, 2, 3, 5, 8, 12, 18, 26, 37, 51, 69, 92, 121, 157, 202, 257, 324, 405, 503, 620, 760, 926, 1122, 1353, 1624, 1941, 2310, 2739, 3235, 3808, 4468, 5226, 6095, 7088, 8221, 9511, 10976, 12638, 14519, 16644, 19041
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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The generating function was found by Moshe Newman.
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REFERENCES
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Nathanson, Melvyn B., Number Theory and semigroups of intermediate growth, Amer. Math. Monthly 106(1999) 666-669
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FORMULA
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Generating function: 1/(1-x)+ x/((1-x)^2 (1-x^2)(1-x^3)(1-x^5)(1-x^7)(1-x^11)...) where the product is over all primes.
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EXAMPLE
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The products of two matrices in A are r.r, r.b, b.r and b.b, that is
{{1, 2}, {0, 1}}, {{2, 0}, {1, 0}}, {{1, 1}, {1, 1}}, {{1, 0}, {1, 0}}.
Of these, the last one, b.b is an element of length one, since it is equal to b. The remainder are elements of length two, hence a(2)=3.
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CROSSREFS
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Sequence in context: A105858 A039899 A039901 this_sequence A058984 A084376 A098693
Adjacent sequences: A121943 A121944 A121945 this_sequence A121947 A121948 A121949
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KEYWORD
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nonn
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AUTHOR
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David Newman (davidsnewman(AT)gmail.com), Sep 04 2006
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