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A089067
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a(n) = 2*a(n-1) + (-1)^n*a(floor(n/2)); a(1)=1.
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4
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1, 3, 5, 13, 23, 51, 97, 207, 401, 825, 1627, 3305, 6559, 13215, 26333, 52873, 105539, 211479, 422557, 845939, 1691053, 3383733, 6765839, 13534983, 27066661, 54139881, 108273203, 216559621, 433106027, 866238387, 1732450441, 3464953755, 6929854637, 13859814813
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OFFSET
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1,2
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LINKS
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FORMULA
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Lim_{n->infinity} a(n)/2^n = 0.8067474....
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EXAMPLE
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a(2) = 2*1 + 1 = 3;
a(3) = 2*3 - 1 = 5;
a(4) = 2*5 + 3 = 13;
a(5) = 2*13 - 3 = 23;
a(6) = 2*23 + 5 = 51;
a(7) = 2*51 - 5 = 97;
...
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PROG
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(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
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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a(31) corrected and terms a(32) and beyond from Andrew Howroyd, Jun 05 2021
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STATUS
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approved
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