%I A084202
%S A084202 1,1,0,1,0,1,1,2,2,4,6,10,16,27,44,75,127,218,375,650,1130,1974,3460,6086,
%T A084202 10736,18993,33685,59882,106683,190446,340611,610243,1095102,1968200,3542468,
%U A084202 6384518,11521308,20815942,37651528,68176596,123574852,224204708,407153894
%V A084202 1,1,0,1,0,1,-1,2,-2,4,-6,10,-16,27,-44,75,-127,218,-375,650,-1130,1974,
               -3460,6086,
%W A084202 -10736,18993,-33685,59882,-106683,190446,-340611,610243,-1095102,1968200,
               -3542468,
%X A084202 6384518,-11521308,20815942,-37651528,68176596,-123574852,224204708,-407153894
%N A084202 G.f. A(x) defined by: A(x)^2 consists entirely of integer coefficients 
               between 1 and 2 (A083952); A(x) is the unique power series solution 
               with A(0)=1.
%C A084202 Limit a(n)/a(n+1) -> r = -0.530852489019085 where A(r)=0.
%H A084202 N. Heninger, E. M. Rains and N. J. A. Sloane, <a href="http://arXiv.org/
               abs/math.NT/0509316">On the Integrality of n-th Roots of Generating 
               Functions</a>, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.
%t A084202 a[n_] := a[n] = Block[{s = Sum[a[i]*x^i, {i, 0, n - 1}]}, If[ IntegerQ@ 
               Last@ CoefficientList[ Series[ Sqrt[s + x^n], {x, 0, n}], x], 1, 
               2]]; Table[a[n], {n, 0, 42}]; CoefficientList[ Series[ Sqrt[ Sum[ 
               a[i]*x^i, {i, 0, 42}]], {x, 0, 42}], x] (* Robert G. Wilson v (rgwv(AT)rgwv.com), 
               Nov 11 2007 *)
%Y A084202 Cf. A083952, A084203-A084212.
%Y A084202 Sequence in context: A006355 A055389 A163733 this_sequence A053637 A000016 
               A060553
%Y A084202 Adjacent sequences: A084199 A084200 A084201 this_sequence A084203 A084204 
               A084205
%K A084202 sign
%O A084202 0,8
%A A084202 Paul D. Hanna (pauldhanna(AT)juno.com), May 19 2003