A005005 Davenport-Schinzel numbers of degree n on 4 symbols.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• easy

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

Crossrefs

A row of the array in A259874.

Programs

Mathematica

LinearRecurrence[{1,1,-1},{1,4,7,12,16,23,28},60] (* Harvey P. Dale, Jul 22 2021 *)

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)

Extensions

Title improved and more terms from Sean A. Irvine, Feb 19 2016