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 A343417 #44 Mar 13 2022 09:49:55 %S A343417 1,1,2,6,19,71,300,1370,6563,32272,161700,820166,4198764,21647353, %T A343417 112262033,585049063,3061951973,16084816384,84773694223 %N A343417 a(n) is the number of free polyominoes with k cells and n-k distinguished vertices. %C A343417 This sequence counts "free" polyominoes where holes are allowed. This means that two polyominoes are considered the same if one is a rigid transformation (translation, rotation, reflection or glide reflection) of the other. %C A343417 A000105(n) <= a(n) <= A343577(n). %C A343417 For an ordinary, asymmetrical polyomino, the number of free polyominoes with d distinguished cells is equal to C(v,d), where v is the number of vertices of the polyomino, and C is the binomial coefficient (A007318). - _John Mason_, Mar 11 2022 %H A343417 Peter Kagey, <a href="/A343417/a343417_1.hs.txt">Haskell program for computing sequence</a>. %e A343417 For n = 3, the a(3) = 6 polyominoes with k cells and 3-k distinguished vertices are: %e A343417 +---+ *---+ +---+ %e A343417 | | | | | | %e A343417 + +---+ +---+---+---+ + + * + *---+ *---+ %e A343417 | | | | | | | | | | | | %e A343417 +---+---+, +---+---+---+, +---+, +---+, *---+, +---*, %e A343417 where distinguished vertices are marked with asterisks. %e A343417 For n = 4, a(4) = 19 because there are A000105(4) = 5 polyominoes with four cells and no distinguished vertices, 7 polyominoes with three cells and one distinguished vertex, 6 polyominoes with two cells and two distinguished vertices, and 1 polyomino with one cell and three distinguished vertices. %Y A343417 Cf. A000105, A343577. %K A343417 nonn,more,hard %O A343417 0,3 %A A343417 _Peter Kagey_, Apr 15 2021 %E A343417 a(11)-a(18) from _John Mason_, Mar 11 2022