%I A061348
%S A061348 2,4,20,208,5728,351616,44772352,11453771776,5864078802944,6004800040206336,
%T A061348 12297829416834170880,50371909152808594571264,412646679762074900658913280,
%U A061348 6760803201217259503457555972096,221537999297485988040673580072042496
%N A061348 Consider a (solid) triangle with n cells on each edge, for a total of 
               n(n+1)/2 cells; a(n) is number of ways of labeling cells with 0's 
               and 1's; triangle may be rotated and turned over.
%F A061348 See Maple code for formula.
%e A061348 a(2) = 4, the labelings being {000}, {001}, 011}, {111}. Some of the 
               20 solutions for n=3 are as follows:
%e A061348 ..0......1.......0......1.......1.......1.......0
%e A061348 .0.0....0.0.....1.0....1.0.....0.0.....0.0.....1.1
%e A061348 0.0.0..0.0.0...0.0.0..0.0.0...1.0.0...0.1.0...0.0.0
%e A061348 The first solution for n = 4 is
%e A061348 ...0
%e A061348 ..0.0
%e A061348 .0.0.0
%e A061348 0.0.0.0
%p A061348 A061348 := proc(n) local t1,t,v,a; a := n*(n+1)/2; t := floor((n+2)/3); 
               v := floor((n+1)/2); if n mod 3 = 1 then t1 := n*(n+1)/6+2/3; else 
               t1 := n*(n+1)/6; fi; (1/6)*(2^a + 2*2^t1+3*2^(a/2+v/2)); end; # from 
               Burnside's Lemma
%Y A061348 Cf. A061709.
%Y A061348 Sequence in context: A052573 A110371 A120388 this_sequence A127103 A059831 
               A064493
%Y A061348 Adjacent sequences: A061345 A061346 A061347 this_sequence A061349 A061350 
               A061351
%K A061348 nonn,easy,nice
%O A061348 1,1
%A A061348 Michel ten Voorde (seqfan(AT)tenvoorde.org) Jun 08 2001
%E A061348 Formula and more terms from N. J. A. Sloane (njas(AT)research.att.com), 
               Jun 20, 2001