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A259874 Array read by antidiagonals upwards: Davenport-Schinzel numbers T(n,k), n >= 1, k >= 1. 6

%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

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Last modified March 28 05:02 EDT 2024. Contains 371235 sequences. (Running on oeis4.)