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A099855
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a(n) = n*2^n - 2^(n/2)*sin(Pi*n/4).
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3
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0, 1, 6, 22, 64, 164, 392, 904, 2048, 4592, 10208, 22496, 49152, 106560, 229504, 491648, 1048576, 2227968, 4718080, 9960960, 20971520, 44041216, 92276736, 192940032, 402653184, 838856704, 1744822272, 3623870464, 7516192768
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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G.f.: x/((1-2*x+2*x^2)*(1-4*x+4*x^2)).
a(n) = Sum_{k=0..n} 2^(k/2)*sin(Pi*k/4)*2^(n-k)*(n-k+1).
a(n) = 6*a(n-1) - 14*a(n-2) + 16*a(n-3) - 8*a(n-4).
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MATHEMATICA
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LinearRecurrence[{6, -14, 16, -8}, {0, 1, 6, 22}, 30] (* Harvey P. Dale, Mar 22 2018 *)
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PROG
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(Magma) I:=[0, 1, 6, 22]; [n le 4 select I[n] else 6*Self(n-1) -14*Self(n-2) +16*Self(n-3) -8*Self(n-4): n in [1..51]]; // G. C. Greubel, Apr 20 2023
(SageMath)
@CachedFunction
if (n<5): return (0, 1, 6, 22, 64)[n]
else: return 6*a(n-1) - 14*a(n-2) + 16*a(n-3) - 8*a(n-4)
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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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