cp's OEIS Frontend

A332050 Number of ways to arrange Palago tiles in a triangle of side length n, up to rotation, reflection, and swapping colors.

%I A332050 #15 Feb 07 2020 21:09:51
%S A332050 1,1,7,129,9882,2391930,1743402771,3812799008214,25015772571200361,
%T A332050 492385451093553791610,29074868501520453489499806,
%U A332050 5150525730438768829942800034449,2737200544710109691113626131721984885,4363981784043856212945753449232929426200329
%N A332050 Number of ways to arrange Palago tiles in a triangle of side length n, up to rotation, reflection, and swapping colors.
%C A332050 A Palago tile is a hexagonal tile with four regions of alternating colors. See links for illustrations.
%H A332050 Peter Kagey, <a href="/A332050/b332050.txt">Table of n, a(n) for n = 0..64</a>
%H A332050 Code Golf Stack Exchange, <a href="https://codegolf.stackexchange.com/q/193011/53884">Counting creatures on a hexagonal tiling</a>
%H A332050 Peter Kagey, <a href="/A332050/a332050.pdf">Example of for n = 2</a>.
%F A332050 a(n) = (3^A000217(n) + 3*3^A002620(n) + 2*3^A007997(n+4))/6 if n = 1 (mod 3), and
%F A332050 a(n) = (3^A000217(n) + 3*3^A002620(n))/6 otherwise.
%t A332050 a[n_] = (3^Binomial[n + 1, 2] +
%t A332050     3*3^((Binomial[n + 1, 2] - Ceiling[n/2])/2) +
%t A332050     If[Mod[n, 3] == 1, 0, 2*3^(Binomial[n + 1, 2]/3)])/6
%Y A332050 Cf. A000217, A002620, A007997.
%Y A332050 Cf. A325936.
%K A332050 nonn
%O A332050 0,3
%A A332050 _Peter Kagey_, Feb 06 2020