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A117902
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Expansion of (1-x^2-2x^3)/(1-4x^3).
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3
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1, 0, -1, 2, 0, -4, 8, 0, -16, 32, 0, -64, 128, 0, -256, 512, 0, -1024, 2048, 0, -4096, 8192, 0, -16384, 32768, 0, -65536, 131072, 0, -262144, 524288, 0, -1048576, 2097152, 0, -4194304, 8388608, 0, -16777216, 33554432, 0, -67108864, 134217728, 0, -268435456, 536870912, 0, -1073741824
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OFFSET
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0,4
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COMMENTS
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Row sums of number triangle A117901.
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LINKS
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FORMULA
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a(n) = 0^n/2 - (2^(2*n/3)/12)*( 2*cos((2*n+1)*Pi*n/3) + 2*sqrt(3)*sin((2*n+1)*Pi*n/3) -(2^(2/3) + 8)*cos(2*Pi*n/3) - 2^(1/6)*sqrt(6)*sin(2*Pi*n/3) + 2^(2/3) - 2 ).
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MATHEMATICA
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LinearRecurrence[{0, 0, 4}, {1, 0, -1, 2}, 50] (* G. C. Greubel, Oct 09 2021 *)
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PROG
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(Magma) [1] cat [n le 3 select (-1)^(n-1)*(n-1) else 4*Self(n-3): n in [1..50]]; // G. C. Greubel, Oct 09 2021
(Sage)
def A133851(n): return 4^(n/3) if (n%3==0) else 0
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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STATUS
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approved
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