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A100132
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a(n) = Sum_{k=0..floor(n/4)} C(n-2k,2k) * 2^(n-3k).
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4
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1, 2, 4, 8, 18, 44, 112, 288, 740, 1896, 4848, 12384, 31624, 80752, 206208, 526592, 1344784, 3434272, 8770368, 22397568, 57198368, 146071744, 373034240, 952645120, 2432840256, 6212924032, 15866403584, 40519208448, 103476899968
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OFFSET
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0,2
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COMMENTS
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Binomial transform of 1,1,1,1,3,3,7,7,41,... (g.f. (1-x)(1+x)^2/(1-2x^2-x^4)).
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LINKS
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FORMULA
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G.f.: (1-2x)/((1-2x)^2-2x^4).
a(n) = 4*a(n-1) - 4*a(n-2) + 2*a(n-3).
a(n) = Sum_{k=0..floor(n/2)} C(n-k, k)2^(n-3k/2)(1+(-1)^k)/2. - Paul Barry, Jan 22 2005
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MATHEMATICA
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LinearRecurrence[{4, -4, 0, 2}, {1, 2, 4, 8}, 30] (* Harvey P. Dale, Jun 07 2016 *)
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PROG
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(PARI) a(n) = sum(k=0, n\4, binomial(n-2*k, 2*k)*2^(n-3*k)); \\ Michel Marcus, Oct 09 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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STATUS
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approved
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