A324000 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).

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

Offset

0,2

Comments

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).

Links

Table of n, a(n) for n=0..53.

T. Tarnai, Baskets, 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.

T. Tarnai, F. Kovács, P. W. Fowler, and S. D. Guest, Wrapping the cube and other polyhedra, Proc. Roy. Soc. A 468(2145) (2012), 2652-2666. DOI: 10.1098/rspa.2012.0116.

Felicity Wood, Illustration for T(1,5) = 4. [Included with permission.]

Example

The array begins:
  0,3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,...
  3,4,6,4,3,4,6,4,3,4,6,4,3,4,6,4,3,4,6,4,...
  6,6,8,3,12,3,8,6,6,6,8,3,12,3,8,6,6,6,8,3,...
  9,4,3,12,3,4,18,4,3,12,3,4,9,4,3,12,3,4,18,4,...
  12,3,12,3,16,6,6,3,24,3,6,6,16,3,12,3,12,3,12,3,...
  ...
The first few antidiagonals are:
  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,
  ...
The illustration for T(1,5)=4 shows a basket constructed and photographed by Felicity Wood of the Oxfordshire Basketmakers Association.

Crossrefs

Rows 2 and 3 are A324001, A324002.

Sequence in context: A051472 A257957 A369501 * A048149 A155169 A144624

Adjacent sequences: A323997 A323998 A323999 * A324001 A324002 A324003

Keyword

nonn,tabl,more

Author

N. J. A. Sloane, Feb 15 2019

Status

approved