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Triangle read by rows: number of balanced twills with 2n harnesses and maximum float length k (1 <= k <= n).
1

%I #21 Mar 21 2021 13:08:27

%S 1,1,1,1,1,1,1,3,2,1,1,4,5,2,1,1,9,13,8,3,1,1,14,33,22,11,3,1,1,30,91,

%T 77,38,15,4,1,1,53,250,246,137,54,19,4,1,1,114,719,852,501,222,79,24,

%U 5,1

%N Triangle read by rows: number of balanced twills with 2n harnesses and maximum float length k (1 <= k <= n).

%D J. A. Hoskins, C. E. Praeger and A. P. Street, Balanced twills with bounded float length, Congress. Numerantium, 40 (1983), 77-89.

%H Janet Anne Hoskins, <a href="https://hdl.handle.net/1993/28925">Isonemal arrays and textile computer graphics</a>, Thesis, 1985. See p. 50.

%H J. A. Hoskins, C. E. Praeger and A. P. Street, <a href="/A006840/a006840.pdf">Balanced twills with bounded float length</a>, Congress. Numerantium, 40 (1983), 77-89. (Annotated scanned copy)

%e Triangle begins:

%e 1;

%e 1, 1;

%e 1, 1, 1;

%e 1, 3, 2, 1;

%e 1, 4, 5, 2, 1;

%e 1, 9, 13, 8, 3, 1;

%e 1, 14, 33, 22, 11, 3, 1;

%e 1, 30, 91, 77, 38, 15, 4, 1;

%e 1, 53, 250, 246, 137, 54, 19, 4, 1;

%e 1, 114, 719, 852, 501, 222, 79, 24, 5, 1;

%e ...

%Y Row sums are A006840.

%K nonn,tabl

%O 1,8

%A _N. J. A. Sloane_, Jun 27 2015