OFFSET
0,8
COMMENTS
T(k,n) is the maximum number of regions the plane can be divided into by drawing n k-armed long-legged V's.
LINKS
Paolo Xausa, Table of n, a(n) for n = 0..11324 (first 150 antidiagonals, flattened).
David O. H. Cutler, Jonas Karlsson, and Neil J. A. Sloane, Cutting a Pancake with an Exotic Knife, arXiv:2511.15864[math.CO], v3, April 19 2026.
N. J. A. Sloane, Illustration for T(3,2) = 14.
N. J. A. Sloane, Illustration for T(3,3) = 34 (a 3-armed V is also known as a Wu).
EXAMPLE
Array begins (the rows are T(0,n>=0),, T(1,n>=0), T(2,n>=0), ...):
1, 1, 1, 1, 1, 1, 1, 1, 1, ...
1, 1, 2, 4, 7, 11, 16, 22, 29, ...
1, 2, 7, 16, 29, 46, 67, 92, 121, ...
1, 3, 14, 34, 63, 101, 148, 204, 269, ...
1, 4, 23, 58, 109, 176, 259, 358, 473, ...
1, 5, 34, 88, 167, 271, 400, 554, 733, ...
1, 6, 47, 124, 237, 386, 571, 792, 1049, ...
1, 7, 62, 166, 319, 521, 772, 1072, 1421, ...
...
The first few antidiagonals are:
1,
1, 1,
1, 1, 1,
1, 2, 2, 1,
1, 3, 7, 4, 1,
1, 4, 14, 16, 7, 1,
1, 5, 23, 34, 29, 11, 1,
1, 6, 34, 58, 63, 46, 16, 1,
1, 7, 47, 88, 109, 101, 67, 22, 1,
...
MATHEMATICA
A386481[k_, n_] := If[k == 0, 1, Binomial[n, 2]*k^2 + n*(k - 1) + 1];
Table[A386481[k - n, n], {k, 0, 12}, {n, 0, k}] (* Paolo Xausa, Nov 22 2025 *)
CROSSREFS
KEYWORD
AUTHOR
N. J. A. Sloane, Aug 11 2025
STATUS
approved
