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A140253
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a(2*n) = 2*(2*4^(n-1)-1) and a(2*n-1) = 2*4^(n-1)-1.
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6
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-1, 1, 2, 7, 14, 31, 62, 127, 254, 511, 1022, 2047, 4094, 8191, 16382, 32767, 65534, 131071, 262142, 524287, 1048574, 2097151, 4194302, 8388607, 16777214, 33554431, 67108862, 134217727, 268435454, 536870911
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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COMMENTS
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The inverse binomial transform is 1, 1, 4, -2, 10, -14, 34, -62 which leads to (-1)^(n+1)*A135440(n).
Also, the decimal representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 673", based on the 5-celled von Neumann neighborhood, initialized with a single black (ON) cell at stage zero. - Robert Price, Jul 23 2017
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REFERENCES
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S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
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LINKS
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FORMULA
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a(n+1) - a(n) = A014551(n); Jacobsthal-Lucas numbers.
a(n+1) - 2*a(n) = A010674(n+1); repeat 3, 0.
a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3) for n>2, a(0) = -1, a(1) = 1, a(2) = 2. - Philippe Deléham, Feb 25 2012
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MAPLE
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MATHEMATICA
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PROG
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(Haskell)
import Data.List (transpose)
a140253 n = a140253_list !! n
a140253_list = -1 : concat
(transpose [a083420_list, map (* 2) a083420_list])
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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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EXTENSIONS
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STATUS
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approved
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