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A308595 a(n) is the number of pentagonal polyiamonds of all orders less than or equal to n. 2
0, 0, 0, 0, 1, 2, 5, 6, 8, 10, 13, 16, 21, 25, 28, 31, 39, 42, 48, 54, 61, 66, 73, 79, 88, 93, 98, 110, 120, 125, 136, 144, 157, 166, 172, 181, 195, 201, 211, 224, 242, 248, 258, 274, 286, 298, 309, 320, 341, 348, 359, 379, 393, 403, 416, 433, 455, 466, 478, 495 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

Given the complete set of pentagonal polyiamonds and a tiling program, all possible pentagonal divisions of a space can be determined. The link section gives an example of the minimum and maximum number of pentagonal divisions of a space with a set of the four smallest pentagonal polyiamonds.

An example of tiling different spaces with a set of 46 different polyiamond tiles is given in the link section below. The idea here is to tile shapes that have a variety of different sides with two tile sets - one that has very few sides (pentagonal) and the other the maximum number of sides (unitary).

LINKS

Table of n, a(n) for n=0..59.

Sean A. Irvine, Java program (github)

Craig Knecht, Pentagonal polyiamond division of a triangle

Craig Knecht, Pentagonal and unitary polyiamond tiling

Walter Trump, Pentagonal polyiamonds

Walter Trump, Simple program

CROSSREFS

Sequence in context: A284777 A081083 A288635 * A104493 A139532 A024798

Adjacent sequences:  A308592 A308593 A308594 * A308596 A308597 A308598

KEYWORD

nonn

AUTHOR

Craig Knecht, Jun 09 2019

STATUS

approved

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Last modified May 13 02:02 EDT 2021. Contains 343836 sequences. (Running on oeis4.)