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A099462
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Expansion of x/(1 - 4*x^2 - 4*x^3).
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2
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0, 1, 0, 4, 4, 16, 32, 80, 192, 448, 1088, 2560, 6144, 14592, 34816, 82944, 197632, 471040, 1122304, 2674688, 6373376, 15187968, 36192256, 86245376, 205520896, 489750528, 1167065088, 2781085696, 6627262464, 15792603136, 37633392640
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OFFSET
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0,4
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COMMENTS
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LINKS
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FORMULA
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a(n) = 4*a(n-2) + 4*a(n-3).
a(n) = Sum_{k=0..floor((n-1)/2)} binomial(k, n-2*k-1)*4^k.
a(n+1) = Sum_{k=0..floor(n/2)} C((n-k)/2, k)*(1+(-1)^(n-k))*2^(n-k). - Paul Barry, Sep 09 2005
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MATHEMATICA
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LinearRecurrence[{0, 4, 4}, {0, 1, 0}, 40] (* G. C. Greubel, Nov 18 2021 *)
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PROG
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(Magma) [n le 3 select (1+(-1)^n)/2 else 4*(Self(n-2) +Self(n-3)): n in [1..41]]; // G. C. Greubel, Nov 18 2021
(Sage)
def a(n): return sum( 4^k*binomial(k, n-2*k-1) for k in (0..(n-1)//2) )
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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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