%I A111282
%S A111282 1,2,6,16,42,110,288,754,1974,5168,13530,35422,92736,242786,635622,
%T A111282 1664080,4356618,11405774,29860704,78176338,204668310,535828592,
%U A111282 1402817466,3672623806,9615053952,25172538050,65902560198,172535142544
%N A111282 Number of permutations avoiding the patterns {1432,2431,3412,3421,4132,
               4231,4312,4321}; number of strong sorting class based on 1432.
%C A111282 a(n-1) is the sum, over all Boolean n-strings, of the product of the 
               lengths of the runs. For example, the Boolean 7-string (0,1,1,0,1,
               1,1) has four runs, whose lengths are 1,2,1 and 3, contributing a 
               product of 6 to a(6). The 4 Boolean 2-strings contribute to a(3) 
               as follows: 00 and 11 both contribute 2 and 01 and 10 both contribute 
               1. - David Callan (callan(AT)stat.wisc.edu), Jul 22 2008
%D A111282 M. Albert, R. Aldred, M. Atkinson, C Handley, D. Holton, D. McCaughan 
               and H. van Ditmarsch, Sorting Classes, Elec. J. of Comb. 12 (2005)
%F A111282 a(n)=3a(n-1)-a(n-2)
%F A111282 a(n)=A025169(n-2), n>1. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Aug 18 2008]
%F A111282 Contribution from Paul Barry (pbarry(AT)wit.ie), Oct 13 2009: (Start)
%F A111282 G.f.: (1-x+x^2)/(1-3x+x^2).
%F A111282 a(n)=F(2n+1)+F(2n-2)+0^n. (End)
%t A111282 a[1] = 1; a[2] = 2; a[3] = 6; a[n_] := a[n] = 3a[n - 1] - a[n - 2]; Table[a[n], 
               {n, 28}] (* Robert G. Wilson v *)
%Y A111282 Sequence in context: A102699 A156664 A025169 this_sequence A115730 A003142 
               A027994
%Y A111282 Adjacent sequences: A111279 A111280 A111281 this_sequence A111283 A111284 
               A111285
%K A111282 nonn
%O A111282 1,2
%A A111282 Len Smiley ( smiley (at) math.uaa.alaska.edu ), Nov 01 2005
%E A111282 More terms from Robert G. Wilson v (rgwv(at)rgwv.com), Nov 04 2005