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

%I A259874 #34 Oct 14 2024 02:55:06
%S A259874 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 A259874 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 A259874 Array read by antidiagonals upwards: Davenport-Schinzel numbers T(n,k), n >= 1, k >= 1.
%C A259874 Named after the English mathematician Harold Davenport (1907-1969) and the Polish mathematician Andrzej Schinzel (1937-2021). - _Amiram Eldar_, Jun 06 2021
%D A259874 R. K. Guy, Unsolved Problems in Number Theory, Springer, 1st edition, 1981. See section E20.
%D A259874 R. G. Stanton and P. H. Dirksen, Davenport-Schinzel sequences, Ars. Combin., 1 (1976), 43-51.
%H A259874 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 A259874 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 A259874 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 A259874 First few antidiagonals:
%e A259874   1;
%e A259874   1,  1;
%e A259874   1,  2,  1;
%e A259874   1,  3,  3,  1;
%e A259874   1,  4,  5,  4,  1;
%e A259874   1,  5,  7,  8,  5,  1;
%e A259874   1,  6,  9, 12, 10,  6,  1;
%e A259874   1,  7, 11, 17, 16, 14,  7,  1;
%e A259874   1,  8, 13, 22, 22, 23, 16,  8,  1;
%e A259874   ...
%e A259874 First few rows:
%e A259874   1,  1,  1,  1,  1,  1, ...
%e A259874   1,  2,  3,  4,  5,  6,  7,  8, ...
%e A259874   1,  3,  5,  8, 10, 14, 16, 20, 22, 26, ...
%e A259874   1,  4,  7, 12, 16, 23, 28, 35, 40, 47, ...
%e A259874   1,  5,  9, 17, 22, 34, 41, 53, 61, 73, ...
%e A259874   ...
%Y A259874 Rows and columns include A005004, A005005, A005006, A002004.
%K A259874 nonn,tabl,more
%O A259874 1,5
%A A259874 _N. J. A. Sloane_, Jul 09 2015
%E A259874 More terms from _Sean A. Irvine_, Feb 21 2016