A300123 Number of ways to tile the diagram of the integer partition with Heinz number n using connected skew partitions.

1, 1, 2, 2, 4, 4, 8, 4, 10, 8, 16, 8, 32, 16, 20, 8, 64, 20, 128, 16, 40, 32, 256, 16, 52, 64, 52, 32, 512, 40, 1024, 16, 80, 128, 104, 40, 2048, 256, 160, 32, 4096, 80, 8192, 64, 104, 512, 16384, 32, 272, 104

Offset

1,3

Comments

The diagram of a connected skew partition is required to be connected as a polyomino but can have empty rows or columns. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

Links

Table of n, a(n) for n=1..50.

Solomon W. Golomb, Tiling with polyominoes, Journal of Combinatorial Theory, 1-2 (1966), 280-296.

Gus Wiseman, The a(25) = 52 connected tilings of (3,3).

Crossrefs

Cf. A000085, A000898, A056239, A006958, A238690, A259479, A259480, A296150, A296561, A297388, A299699, A299925, A299926, A300060, A300118, A300120, A300121, A300122, A300124.

Sequence in context: A292253 A115209 A139210 * A175359 A336125 A353125

Adjacent sequences: A300120 A300121 A300122 * A300124 A300125 A300126

Keyword

nonn

Author

Gus Wiseman, Feb 25 2018

Status

approved