A005005 - OEIS

A005005

Davenport-Schinzel numbers of degree n on 4 symbols.
(Formerly M3305)

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

Table of n, a(n) for n=1..53.

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]

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

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

Adjacent sequences: A005002 A005003 A005004 * A005006 A005007 A005008