%I A147869
%S A147869 1,1,1,3,4,7,11,17,25,41,59,86,125,180,263,382,536,738,1073,1466,2028,
%T A147869 2841,3889,5275,7211,9800,13249,17860,23948,31921,42864,56802,75115,
%U A147869 99788,131239,172870,226789,296404,386745,504939,655227,849628,1101270
%N A147869 A Fernandez-type expansion for Conway's A004001: p(x,n)=Product[x+A004001[n],
               {n,0,Infinity}]; a(n)=Coefficients[(p(x,n)).
%C A147869 The resulting polynomial is equivalent to and 1/q(x) type expansion of 
               q(x)=x^n*f(1/x) and that expansion has a limiting ratio ( largest 
               positive root) near:1.2125507033495728 or smaller: Table[N[a2[[n 
               + 1]]/a2[[n]]], {n, 1, 99}]. This result is interesting, important 
               and new, since nothing except Salems have that low of a ratio.
%F A147869 p(x,n)=Product[x+A004001[n],{n,0,Infinity}]; a(n)=Coefficients[(p(x,n)).
%t A147869 (*A004001*) f[0] = 0; f[1] = 1; f[2] = 1; f[n_] := f[n] = f[f[n - 1]] 
               + f[n - f[n - 1]]; P[x_, n_] := P[x, n] = Product[1 + f[m]*x^m, {m, 
               0, n}]; a2 = CoefficientList[ExpandAll[P[x, 100]], x]; Table[a2[[n]], 
               {n, 1, 100}]
%Y A147869 A147559, A147654, A147655, A004001
%Y A147869 Sequence in context: A166375 A060962 A069950 this_sequence A100581 A093090 
               A000204
%Y A147869 Adjacent sequences: A147866 A147867 A147868 this_sequence A147870 A147871 
               A147872
%K A147869 nonn
%O A147869 0,4
%A A147869 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 16 2008