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Search: id:A153265
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| A153265 |
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a(n) = (-2*I)^n + (2*I)^n + (1/2 + 1/2*I*sqrt(3))^n + (1/2 - 1/2*I*sqrt(3))^n |
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+0
3
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| 4, 1, -9, -2, 31, 1, -126, 1, 511, -2, -2049, 1, 8194, 1, -32769, -2, 131071, 1, -524286, 1, 2097151, -2, -8388609, 1, 33554434, 1, -134217729, -2, 536870911, 1, -2147483646, 1, 8589934591, -2, -34359738369, 1
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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For all n there is an m such that: ||a(n)| - 2^m| <= 2. In the Python program which will be provided, the sequence (a(n)) is given by 4tesseq(X) where X = 1.5'i + .25(ii + jj + kk + ee) is the generating floretion.
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FORMULA
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a(n) = a(n-1) - 5a(n-2) + 4a(n-3) - 4a(n-4); g.f. (1-10*x+12*x^2-16*x^3)/((x^2-x+1)*(4*x^2+1))
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EXAMPLE
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a(4) = 32 + (1/2 + 1/2*I*sqrt(3))^4 + (1/2 - 1/2*I*sqrt(3))^4 = 31 -or- a(4) = a(n-1) - 5a(n-2) + 4a(n-3) - 4a(n-4) = -2 - 5*(-9) + 4*(1) - 4*4 = 31
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MAPLE
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a := n-> (2*I)^n+(-2*I)^n+(1/2+1/2*I*sqrt(3))^n+(1/2-1/2*I*sqrt(3))^n;
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CROSSREFS
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A153266, A153267, A153268
Sequence in context: A080103 A091419 A085383 this_sequence A085691 A055461 A104796
Adjacent sequences: A153262 A153263 A153264 this_sequence A153266 A153267 A153268
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KEYWORD
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easy,sign
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AUTHOR
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Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Dec 22 2008, Dec 31 2008
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