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1, -4, 16, -64, 256, -1024, 4096, -16384, 65536, -262144, 1048576, -4194304, 16777216, -67108864, 268435456, -1073741824, 4294967296, -17179869184, 68719476736, -274877906944, 1099511627776, -4398046511104, 17592186044416, -70368744177664, 281474976710656
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refs;
listen;
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internal format)
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OFFSET
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0,2
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COMMENTS
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Purely real values from the sequence generated by (1 + i)^k where i = sqrt(-1) and k is a real nonnegative integer.
This sequence gives the values of (1 + i)^k when k is a multiple of 4. When k = 2 mod 4, (1 + i)^k is purely imaginary, and when k is odd, (1 + i)^k has both a real and an imaginary part, and abs(Re((1 + i)^k)) = abs(Im((1 + i)^k)).
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LINKS
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FORMULA
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a(n) = (-4)^n.
G.f.: 1/(1 + 4 * x).
a(n) = Sum_{k=0..2*n} (-1)^k*binomial(4*n, 2*k) (see Nunn, p. 9). - Stefano Spezia, Dec 28 2021
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MATHEMATICA
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PROG
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(PARI) vector(100, n, n--; (-4)^n) \\ Altug Alkan, Oct 05 2015
(PARI) lista(nn) = for (n=0, nn, z = (1+I)^n; if (imag(z)==0, print1(real(z), ", "))); \\ Michel Marcus, Nov 01 2015
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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