%I #30 Oct 02 2023 02:38:24
%S 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,
%T 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
%N Array read by antidiagonals upwards: Davenport-Schinzel numbers T(n,k), n >= 1, k >= 1.
%C Named after the English mathematician Harold Davenport (1907-1969) and the Polish mathematician Andrzej Schinzel (1937-2021). - _Amiram Eldar_, Jun 06 2021
%D R. G. Stanton and P. H. Dirksen, Davenport-Schinzel sequences, Ars. Combin., 1 (1976), 43-51.
%H Harold Davenport and Andrzej Schinzel, <a href="https://www.jstor.org/stable/2373068">A combinatorial problem connected with differential equations</a>, American Journal of Mathematics, Vol. 87, No. 3 (1965), pp. 684-694.
%H R. G. Stanton and P. H. Dirksen, <a href="/A002004/a002004.pdf">Davenport-Schinzel sequences</a>, Ars. Combin., Vol. 1 (1976), pp. 43-51. [Annotated scanned copy]
%H R. G. Stanton and P. H. Dirksen, <a href="/A002004/a002004_1.pdf">Davenport-Schinzel sequences</a>, Ars. Combin., Vol. 1 (1976), pp. 43-51. [Annotated scanned copy, different annotations from one above]
%e First few antidiagonals:
%e 1;
%e 1, 1;
%e 1, 2, 1;
%e 1, 3, 3, 1;
%e 1, 4, 5, 4, 1;
%e 1, 5, 7, 8, 5, 1;
%e 1, 6, 9, 12, 10, 6, 1;
%e 1, 7, 11, 17, 16, 14, 7, 1;
%e 1, 8, 13, 22, 22, 23, 16, 8, 1;
%e ...
%e First few rows:
%e 1, 1, 1, 1, 1, 1, ...
%e 1, 2, 3, 4, 5, 6, 7, 8, ...
%e 1, 3, 5, 8, 10, 14, 16, 20, 22, 26, ...
%e 1, 4, 7, 12, 16, 23, 28, 35, 40, 47, ...
%e 1, 5, 9, 17, 22, 34, 41, 53, 61, 73, ...
%e ...
%Y Rows and columns include A005004, A005005, A005006, A002004.
%K nonn,tabl,more
%O 1,5
%A _N. J. A. Sloane_, Jul 09 2015
%E More terms from _Sean A. Irvine_, Feb 21 2016
|