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A307889 G.f. A(x) satisfies: A(x) = 1 + x*A(x^2)/(1 - x)^2.

%I A307889 #10 May 03 2019 11:52:41
%S A307889 1,1,2,4,6,10,14,22,30,44,58,82,106,144,182,242,302,392,482,616,750,
%T A307889 942,1134,1408,1682,2062,2442,2966,3490,4196,4902,5850,6798,8048,9298,
%U A307889 10940,12582,14706,16830,19570,22310,25800,29290,33722,38154,43720,49286,56260,63234,71890,80546
%N A307889 G.f. A(x) satisfies: A(x) = 1 + x*A(x^2)/(1 - x)^2.
%H A307889 Robert Israel, <a href="/A307889/b307889.txt">Table of n, a(n) for n = 0..10000</a>
%p A307889 N:=100: # to get a(1)..a(N)
%p A307889 A:= 1:
%p A307889 for iter from 1 do
%p A307889   B:= convert(series(1 + x*subs(x=x^2,A)/(1-x)^2, x, N+1),polynom);
%p A307889   if B = A then break fi;
%p A307889   A:= B;
%p A307889 od:
%p A307889 seq(coeff(A,x,j),j=0..N); # _Robert Israel_, May 03 2019
%t A307889 terms = 50; A[_] = 0; Do[A[x_] = 1 + x A[x^2]/(1 - x)^2 + O[x]^(terms + 1) // Normal, terms + 1]; CoefficientList[A[x], x]
%t A307889 a[0] = 1; a[1] = 1; a[2] = 1; a[n_] := a[n] = 2 a[n - 1] - a[n - 2] + a[Floor[n/2]]; Join[{1, 1}, Differences[Table[2 a[n + 1], {n, 50}]]]
%Y A307889 Cf. A001906, A040039, A298414.
%K A307889 nonn
%O A307889 0,3
%A A307889 _Ilya Gutkovskiy_, May 03 2019