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A089067 a(n) = 2*a(n-1) + (-1)^n*a(floor(n/2)); a(1)=1. 4

%I

%S 1,3,5,13,23,51,97,207,401,825,1627,3305,6559,13215,26333,52873,

%T 105539,211479,422557,845939,1691053,3383733,6765839,13534983,

%U 27066661,54139881,108273203,216559621,433106027,866238387,1732450441,3464953755,6929854637,13859814813

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

%H Andrew Howroyd, <a href="/A089067/b089067.txt">Table of n, a(n) for n = 1..1000</a>

%F Lim_{n->infinity} a(n)/2^n = 0.8067474....

%F 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 a(2) = 2*1 + 1 = 3;

%e a(3) = 2*3 - 1 = 5;

%e a(4) = 2*5 + 3 = 13;

%e a(5) = 2*13 - 3 = 23;

%e a(6) = 2*23 + 5 = 51;

%e a(7) = 2*51 - 5 = 97;

%e ...

%o (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 Cf. A011782.

%K easy,nonn

%O 1,2

%A _Philippe Deléham_, Dec 02 2003

%E a(31) corrected and terms a(32) and beyond from _Andrew Howroyd_, Jun 05 2021

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Last modified September 24 15:58 EDT 2022. Contains 356943 sequences. (Running on oeis4.)