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A108485
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Sum binomial(2n-2k,2k)2^(n-k), k=0..floor(n/2).
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1
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1, 2, 6, 32, 140, 600, 2632, 11520, 50320, 219936, 961376, 4201984, 18366144, 80275840, 350873728, 1533616128, 6703206656, 29298713088, 128060286464, 559732334592, 2446506216448, 10693312305152, 46738866751488
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OFFSET
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0,2
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COMMENTS
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In general, sum{k=0..floor(n/2), C(2n-2k,2k)a^k*b^(n-k)} has expansion (1-bx-abx^2)/(1-2bx-(2ab-b^2)x^2-2ab^2*x^3+(ab)^2*x^4).
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LINKS
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FORMULA
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G.f.: (1-2x-2x^2)/(1-4x-8x^3+4x^4); a(n)=4a(n-1)+8a(n-3)-4a(n-4).
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MATHEMATICA
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LinearRecurrence[{4, 0, 8, -4}, {1, 2, 6, 32}, 40] (* or *) CoefficientList[Series[(1-2x-2x^2)/(1-4x-8x^3+4x^4), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 26 2012 *)
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PROG
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(Magma) I:=[1, 2, 6, 32]; [n le 4 select I[n] else 4*Self(n-1)+8*Self(n-3)-4*Self(n-4): n in [1..30]]; // Vincenzo Librandi. Jun 26 2012
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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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