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A335713
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The sum of the sizes of the largest fixed points over all compositions of n.
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3
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1, 1, 3, 7, 16, 34, 73, 155, 324, 674, 1393, 2861, 5852, 11929, 24239, 49127, 99360, 200598, 404377, 814135, 1637363, 3290067, 6605980, 13255451, 26583994, 53290694, 106787166, 213919062, 428415074, 857794856, 1717201360, 3437092882, 6878672565, 13764822699
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OFFSET
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1,3
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REFERENCES
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M. Archibald, A. Blecher and A. Knopfmacher, Fixed points in compositions and words, accepted by the Journal of Integer Sequences.
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LINKS
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FORMULA
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G.f.: Sum_{j>=1} (x/(1-x))^(j-1) j x^j Sum_{k>=j} Product_{i=j+1..k} (x/(1-x) - x^i).
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EXAMPLE
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For n=3 the a(3)=3 values are the first 1 in the composition 111 and the 2 in the composition 12 (the compositions 21 and 3 do not have any fixed points).
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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