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A089067 a(n) = 2*a(n-1) + (-1)^n*a(floor(n/2)); a(1)=1.

%I A089067 #13 Jun 05 2021 16:43:57
%S A089067 1,3,5,13,23,51,97,207,401,825,1627,3305,6559,13215,26333,52873,
%T A089067 105539,211479,422557,845939,1691053,3383733,6765839,13534983,
%U A089067 27066661,54139881,108273203,216559621,433106027,866238387,1732450441,3464953755,6929854637,13859814813
%N A089067 a(n) = 2*a(n-1) + (-1)^n*a(floor(n/2)); a(1)=1.
%H A089067 Andrew Howroyd, <a href="/A089067/b089067.txt">Table of n, a(n) for n = 1..1000</a>
%F A089067 Lim_{n->infinity} a(n)/2^n = 0.8067474....
%F A089067 G.f. A(x) satisfies (1 + A(x))/(1 + A(x^2)) = (1-x)/(1-2*x). - _Gary W. Adamson_, Feb 18 2010, edited by _Andrew Howroyd_, Jun 05 2021
%e A089067 a(2) = 2*1  + 1 =  3;
%e A089067 a(3) = 2*3  - 1 =  5;
%e A089067 a(4) = 2*5  + 3 = 13;
%e A089067 a(5) = 2*13 - 3 = 23;
%e A089067 a(6) = 2*23 + 5 = 51;
%e A089067 a(7) = 2*51 - 5 = 97;
%e A089067 ...
%o A089067 (PARI) seq(n)={my(a=vector(n)); a[1]=1; for(n=2, n, a[n] = 2*a[n-1] + (-1)^n*a[floor(n/2)]); a} \\ _Andrew Howroyd_, Jun 05 2021
%Y A089067 Cf. A011782.
%K A089067 easy,nonn
%O A089067 1,2
%A A089067 _Philippe Deléham_, Dec 02 2003
%E A089067 a(31) corrected and terms a(32) and beyond from _Andrew Howroyd_, Jun 05 2021