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A335712
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The sum of the sizes of the minimal fixed points over all compositions of n.
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3
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1, 1, 2, 6, 12, 27, 54, 115, 237, 486, 997, 2030, 4122, 8350, 16881, 34054, 68609, 138052, 277500, 557328, 1118546, 2243589, 4498004, 9014053, 18058159, 36166338, 72415886, 144970116, 290170091, 580721926, 1162077483, 2325206168, 4652155420, 9307199819
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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} (Product_{i=1..j-1} (x/(1-x)-x^i)) j x^j (1-x)/(1-2x).
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EXAMPLE
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Example: For n=3 the a(3)=2 values are the first 1s in 111 and 12 (the other compositions 21 and 3 do not have any fixed points).
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PROG
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(PARI) my(N=44, x='x+O('x^N)); Vec( sum(j=1, N, prod(i=1, j-1, (x/(1-x)-x^i) ) *j*x^j * (1-x)/(1-2*x) ) ) \\ Joerg Arndt, Jun 18 2020
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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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