A259874 Array read by antidiagonals upwards: Davenport-Schinzel numbers T(n,k), n >= 1, k >= 1.

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 5, 4, 1, 1, 5, 7, 8, 5, 1, 1, 6, 9, 12, 10, 6, 1, 1, 7, 11, 17, 16, 14, 7, 1, 1, 8, 13, 22, 22, 23, 16, 8, 1, 1, 9, 15, 27, 29, 34, 28, 20, 9, 1, 1, 10, 17, 32

Offset: 1

Author

N. J. A. Sloane, Jul 09 2015

Keywords

• nonn
• tabl
• more

Comments

Named after the English mathematician Harold Davenport (1907-1969) and the Polish mathematician Andrzej Schinzel (1937-2021). - Amiram Eldar, Jun 06 2021

Examples

			First few antidiagonals:
  1;
  1,  1;
  1,  2,  1;
  1,  3,  3,  1;
  1,  4,  5,  4,  1;
  1,  5,  7,  8,  5,  1;
  1,  6,  9, 12, 10,  6,  1;
  1,  7, 11, 17, 16, 14,  7,  1;
  1,  8, 13, 22, 22, 23, 16,  8,  1;
  ...
First few rows:
  1,  1,  1,  1,  1,  1, ...
  1,  2,  3,  4,  5,  6,  7,  8, ...
  1,  3,  5,  8, 10, 14, 16, 20, 22, 26, ...
  1,  4,  7, 12, 16, 23, 28, 35, 40, 47, ...
  1,  5,  9, 17, 22, 34, 41, 53, 61, 73, ...
  ...
		

References

• R. K. Guy, Unsolved Problems in Number Theory, Springer, 1st edition, 1981. See section E20.
• R. G. Stanton and P. H. Dirksen, Davenport-Schinzel sequences, Ars. Combin., 1 (1976), 43-51.

Links

• Harold Davenport and Andrzej Schinzel, A combinatorial problem connected with differential equations, American Journal of Mathematics, Vol. 87, No. 3 (1965), pp. 684-694.
• R. G. Stanton and P. H. Dirksen, Davenport-Schinzel sequences, Ars. Combin., Vol. 1 (1976), pp. 43-51. [Annotated scanned copy]
• R. G. Stanton and P. H. Dirksen, Davenport-Schinzel sequences, Ars. Combin., Vol. 1 (1976), pp. 43-51. [Annotated scanned copy, different annotations from one above]

Crossrefs

Rows and columns include A005004, A005005, A005006, A002004.

Extensions

More terms from Sean A. Irvine, Feb 21 2016