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A005005 Davenport-Schinzel numbers of degree n on 4 symbols.
(Formerly M3305)
1
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)
OFFSET
1,2
REFERENCES
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.
LINKS
R. G. Stanton and P. H. Dirksen, Davenport-Schinzel sequences, Ars. Combin., 1 (1976), 43-51. [Annotated scanned copy]
R. G. Stanton and P. H. Dirksen, Davenport-Schinzel sequences, Ars. Combin., 1 (1976), 43-51. [Annotated scanned copy, different annotations from one above]
FORMULA
For n > 4, a(2*n) = 12 * n - 13 and a(2*n+1) = 12 * n - 14. - Sean A. Irvine, Feb 19 2016
From Chai Wah Wu, Jun 17 2020: (Start)
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)
MATHEMATICA
LinearRecurrence[{1, 1, -1}, {1, 4, 7, 12, 16, 23, 28}, 60] (* Harvey P. Dale, Jul 22 2021 *)
CROSSREFS
A row of the array in A259874.
Sequence in context: A310781 A310782 A232424 * A227589 A310783 A310784
KEYWORD
nonn,nice,easy
AUTHOR
EXTENSIONS
Title improved and more terms from Sean A. Irvine, Feb 19 2016
STATUS
approved

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Last modified March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)