This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A383908 #17 Jun 06 2025 08:35:32 %S A383908 1,3,3,7,23,69,228,766,2642,9309,33382,120629,439752,1613135,5953061, %T A383908 22075011,82204128,307213215,1151820825,4330858682,16326297768, %U A383908 61690058385 %N A383908 Number of generalized polyforms with n cells on the snub trihexagonal tiling. %C A383908 A generalized polyform on the snub trihexagonal tiling with n-cells is a collection of n faces connected edgewise. Two polyforms are considered the same they are related by an isometry (translation and/or rotation) of the snub trihexagonal tiling. %H A383908 Peter Kagey, <a href="/A383908/a383908.pdf">Illustration of a(1)-a(4)</a>. %H A383908 Wikipedia, <a href="https://en.wikipedia.org/wiki/Snub_trihexagonal_tiling">Snub trihexagonal tiling</a> %e A383908 For n=1, the a(1) = 3 generalized polyforms are the three types of faces: hexagons, hexagon-adjacent triangles, and hexagon-nonadjacent triangles. %e A383908 For n=2, the a(2) = 3 generalized polyforms are %e A383908 (1) a hexagon with a hexagon-adjacent triangle, %e A383908 (2) a hexagon-adjacent triangle with a hexagon-nonadjacent triangle, and %e A383908 (3) two hexagon-adjacent triangles. %Y A383908 Analogous for other tilings: A000105 (square), A000228 (hexagonal), A000577 (triangular), A197156 (prismatic pentagonal), A197159 (floret pentagonal), A197459 (rhombille), A197462 (kisrhombille), A197465 (tetrakis square), A309159 (snub square), A343398 (trihexagonal), A343406 (truncated hexagonal), A343577 (truncated square), A344211 (rhombitrihexagonal), A344213 (truncated trihexagonal). %K A383908 nonn,more,hard %O A383908 0,2 %A A383908 _Peter Kagey_, May 14 2025 %E A383908 a(12)-a(21) from _Bert Dobbelaere_, Jun 05 2025