A328081 Irregular triangle read by rows: T(n,k), n >= 0, k >= 1, = number of cells of area k/t^2 in generation n of Jim Conant's iterative dissection of a square, where t = 2^ceiling(n/2).

1, 0, 2, 2, 1, 0, 2, 0, 3, 4, 3, 2, 0, 6, 0, 4, 0, 4, 0, 0, 0, 0, 0, 1, 10, 7, 5, 2, 1, 2

Offset

0,3

Comments

This tiling is described in A328078. At generation n, the construction requires that each edge of the square be divided into t = 2^ceiling(n/2) segments. Then 1/t^2 is the area of the smallest possible region at generation n.

Sum_k T(n,k) = A328078(n), Sum_k k*T(n,k) = 4^ceiling(n/2).

Links

Table of n, a(n) for n=0..29.

Jim Conant, Illustration for A328078(4) = 9.

Example

Start of triangle (the rows are labeled by n = 0,1,2,... and the columns by k = 1,2,3,...):
1,
0,2,
2,1,
0,2,0,3,
4,3,2, (See the illustration for n=4: there are 4 regions of area 1/16, 3 of area 2/16, and 2 of area 3/16.)
0,6,0,4,0,4,0,0,0,0,0,1,
10,7,5,2,1,2,
...

Crossrefs

Cf. A328078.

Sequence in context: A323077 A334201 A257400 * A194853 A309866 A287150

Adjacent sequences: A328078 A328079 A328080 * A328082 A328083 A328084

Keyword

nonn,tabf,more

Author

N. J. A. Sloane, Oct 13 2019

Status

approved