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A005005
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Davenport-Schinzel numbers of degree n on 4 symbols.
(Formerly M3305)
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1
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1, 4, 7, 12, 16, 23, 28, 35, 40, 47, 52, 59, 64, 71, 76, 83, 88, 95, 100, 107, 112, 119, 124, 131, 136, 143, 148, 155, 160, 167, 172, 179, 184, 191, 196, 203, 208, 215, 220, 227, 232, 239, 244, 251, 256, 263, 268, 275, 280, 287, 292, 299, 304
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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REFERENCES
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R. K. Guy, Unsolved Problems in Number Theory, E20.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
R. G. Stanton and P. H. Dirksen, Davenport-Schinzel sequences, Ars. Combin., 1 (1976), 43-51.
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LINKS
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R. G. Stanton and P. H. Dirksen, Davenport-Schinzel sequences, Ars. Combin., 1 (1976), 43-51. [Annotated scanned copy, different annotations from one above]
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FORMULA
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For n > 4, a(2*n) = 12 * n - 13 and a(2*n+1) = 12 * n - 14. - Sean A. Irvine, Feb 19 2016
a(n) = a(n-1) + a(n-2) - a(n-3) for n > 7.
G.f.: x*(x^2 + x + 1)*(x^4 + x^3 - x^2 + 2*x + 1)/((x - 1)^2*(x + 1)). (End)
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MATHEMATICA
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LinearRecurrence[{1, 1, -1}, {1, 4, 7, 12, 16, 23, 28}, 60] (* Harvey P. Dale, Jul 22 2021 *)
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CROSSREFS
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KEYWORD
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nonn,nice,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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