A324000 - OEIS

%I #28 Feb 24 2019 12:10:18

%S 0,3,3,6,4,6,9,6,6,9,12,4,8,4,12,15,3,3,3,3,15,18,4,12,12,4,18,21,6,3,

%T 3,3,3,6,21,24,4,8,4,16,4,8,4,24,27,3,6,18,6,6,18,6,3,27

%N Array read by antidiagonals: T(n,k) (n>=0, k>=0) = number of closed strands in an (n,k)-wrapping of the cube (or basket).

%C Row n of the array is periodic with period length 4n. The periodic parts are palindromic (if we include the first term of the next period). For further properties see Tarnai (2006) and Tarnai et al. (2012).

%H T. Tarnai, <a href="http://me.bme.hu/sites/default/files/page/Baskets.pdf">Baskets</a>, in Proceedings of the IASS-APCS 2006 International Symposium: New Olympics New Shell and Spatial Structures, CD-ROM, IASS and Beijing University of Technology, China, 2006, Paper No. IL09, 8 pp. See Table 1.

%H T. Tarnai, F. Kovács, P. W. Fowler, and S. D. Guest, <a href="https://doi.org/10.1098/rspa.2012.0116">Wrapping the cube and other polyhedra</a>, Proc. Roy. Soc. A 468(2145) (2012), 2652-2666. DOI: 10.1098/rspa.2012.0116.

%H Felicity Wood, <a href="/A324000/a324000_1.jpg">Illustration for T(1,5) = 4</a>. [Included with permission.]

%e The array begins:

%e   0,3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,...

%e   3,4,6,4,3,4,6,4,3,4,6,4,3,4,6,4,3,4,6,4,...

%e   6,6,8,3,12,3,8,6,6,6,8,3,12,3,8,6,6,6,8,3,...

%e   9,4,3,12,3,4,18,4,3,12,3,4,9,4,3,12,3,4,18,4,...

%e   12,3,12,3,16,6,6,3,24,3,6,6,16,3,12,3,12,3,12,3,...

%e   ...

%e The first few antidiagonals are:

%e   0,

%e   3,3,

%e   6,4,6,

%e   9,6,6,9,

%e   12,4,8,4,12,

%e   15,3,3,3,3,15,

%e   18,4,12,12,4,18,

%e   ...

%e The illustration for T(1,5)=4 shows a basket constructed and photographed by Felicity Wood of the Oxfordshire Basketmakers Association.

%Y Rows 2 and 3 are A324001, A324002.

%K nonn,tabl,more

%O 0,2

%A _N. J. A. Sloane_, Feb 15 2019