%I #21 Jan 13 2023 09:10:58
%S 1,3,5,20,56,225,819,3333,13336,55231,229146,963284,4068503,17301000,
%T 73893082
%N Number of free poly-[3^3.4^2]-tiles (polyhouses) (holes allowed) with n cells.
%D Branko Grünbaum and G. C. Shephard, Tilings and Patterns. W. H. Freeman, New York, 1987, Sections 2.7, 6.2 and 9.4.
%H Peter Kagey, <a href="/A197156/a197156.pdf">Example illustrating that a(3) = 5</a>.
%H Brendan Owen, <a href="http://web.archive.org/web/20061229103147/http://members.optusnet.com.au/polyforms/2dforms/polyhouses/index.htm">Polyhouses</a> (gives a(1)-a(10)).
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Elongated_triangular_tiling#Prismatic_pentagonal_tiling">Prismatic pentagonal tiling</a>
%Y Cf. A197157, A197158.
%Y Analogous for other tilings: A000105 (square), A000228 (hexagonal), A000577 (triangular), A197159 (floret pentagonal), A197459 (rhombille), A197462 (kisrhombille), A197465 (tetrakis square), A309159 (snub square), A343398 (trihexagonal), A343406 (truncated hexagonal), A343577 (truncated square).
%K hard,nonn
%O 1,2
%A _Joseph Myers_, Oct 10 2011