%I A057886
%S A057886 0,0,0,1,1,2,3,5,7,9,13,16,22,25,34,38,50,54,70,75,95,100,125,131,161,
%T A057886 167,203,210,252,259,308,316,372,380,444,453,525,534,615,625,715,725,
%U A057886 825,836,946,957,1078,1090,1222,1234,1378,1391,1547,1560,1729,1743
%N A057886 Number of integer 4-tuples that give the lengths of the sides of a nongenerate 
               quadrilateral with perimeter n.
%D A057886 Related to: T. Jenkyns and E. Muller, Triangular triples from ceilings 
               to floors, Amer. Math. Monthly, 107 (Aug. 2000), 634-639.
%F A057886 Conjecture: a(1)=0 and, for n>1, a(n)=a(n-1)+d(n-1), where d(n)=floor(n/
               4)*floor((n-2)/4) if n is even and d(n)=floor((n+1)/4) if n is odd.
%e A057886 There are five quadrilaterals with perimeter 8, with sides (1,1,3,3), 
               (1,2,2,3), (1,2,3,2), (1,3,1,3) and (2,2,2,2), so a(8)=5.
%t A057886 Needs["DiscreteMath`Combinatorica`"]; Table[s=Select[Partitions[n], Length[ 
               # ]==4 && #[[1]]<Total[Rest[ # ]] &]; cnt=0; Do[cnt=cnt+Length[ListNecklaces[4,
               s[[i]], Dihedral]], {i,Length[s]}]; cnt, {n,50}] - T. D. Noe (noe(AT)sspectra.com), 
               Oct 24 2006
%Y A057886 The Moebius transform is A057887. Cf. A005044.
%Y A057886 Cf. A062890.
%Y A057886 Sequence in context: A080000 A032459 A028870 this_sequence A069999 A035563 
               A028378
%Y A057886 Adjacent sequences: A057883 A057884 A057885 this_sequence A057887 A057888 
               A057889
%K A057886 nonn
%O A057886 1,6
%A A057886 John W. Layman (layman(AT)math.vt.edu), Sep 19 2000
%E A057886 Corrected by T. D. Noe, Oct 24 2006