A308595 - OEIS

A308595

a(n) is the number of pentagonal polyiamonds of all orders less than or equal to n.

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

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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: A344312 A081083 A288635 * A104493 A139532 A024798

Adjacent sequences: A308592 A308593 A308594 * A308596 A308597 A308598

KEYWORD

nonn

AUTHOR

Craig Knecht, Jun 09 2019

STATUS

approved