A333333 Irregular triangle: T(n,k) gives the number of k-polysticks on edges of the n-cube up to isometries of the n-cube, with 0 <= k <= A001787(n).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 4, 9, 14, 19, 16, 9, 4, 1, 1, 1, 1, 1, 3, 7, 21, 72, 269, 994, 3615

Offset

1,11

Links

Table of n, a(n) for n=1..30.

Code Golf Stack Exchange, Counting polyominoes on (hyper-)cubes

Peter Kagey, Examples of T(3,3) through T(3,8).

Wikipedia, Hypercube

Wikipedia, Polystick

Formula

T(n,k) = T(n-1,k) for k < n.

T(n,0) = T(n,1) = T(n,2) = T(n,A001787(n)-1) = T(n,A001787(n)) = 1.

A222192(n) = Sum_{k=0..n*2^(n-1)} T(n,k) - Sum_{k=0..(n-1)*2^(n-2)} T(n-1,k) for n >= 2. - Peter Kagey, Jun 19 2023

Example

Table begins:
n\k| 0  1  2  3  4   5   6    7    8     9 10 11 12 ...
---+---------------------------------------------------
  1| 1, 1;
  2| 1, 1, 1, 1, 1;
  3| 1, 1, 1, 3, 4,  9, 14,  19,  16,    9, 4, 1, 1;
  4| 1, 1, 1, 3, 7, 21, 72, 269, 994, 3615, ...

Crossrefs

Cf. A001787, A222192.

Sequence in context: A342570 A050163 A207016 * A095292 A263821 A007293

Adjacent sequences: A333330 A333331 A333332 * A333334 A333335 A333336

Keyword

nonn,more,tabf

Author

Peter Kagey, Mar 15 2020

Status

approved