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A097111
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Expansion of (1 + 3x - 2x^2 - 12x^3)/(1 - 9x^2 + 20x^4).
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0
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1, 3, 7, 15, 43, 75, 247, 375, 1363, 1875, 7327, 9375, 38683, 46875, 201607, 234375, 1040803, 1171875, 5335087, 5859375, 27199723, 29296875, 138095767, 146484375, 698867443, 732421875, 3527891647, 3662109375, 17773675963, 18310546875
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: 3*(1+x)/(1-5x^2) - 2/(1-4x^2);
a(n) = 9*a(n-2) - 20*a(n-4);
a(n) = (3/2 + 3*sqrt(5)/10)*(sqrt(5))^n + (3/2 - 3*sqrt(5)/10)*(-sqrt(5))^n - 2^(n+1)*(1+(-1)^n)/2;
a(n) = Sum_{k=0..n} binomial(floor(n/2), floor(k/2))*2^k.
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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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STATUS
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approved
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