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A140966
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a(n) = (5 + (-2)^n)/3.
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14
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2, 1, 3, -1, 7, -9, 23, -41, 87, -169, 343, -681, 1367, -2729, 5463, -10921, 21847, -43689, 87383, -174761, 349527, -699049, 1398103, -2796201, 5592407, -11184809, 22369623, -44739241, 89478487, -178956969, 357913943
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OFFSET
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0,1
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COMMENTS
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Inverse binomial transform of A048573.
This is an example of the case k=-1 of sequences with recurrences a(n) = k*a(n-1) + (k+3)*a(n-2) - (2*k+2)*a(n-3).
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LINKS
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FORMULA
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a(n) = -a(n-1) + 2*a(n-2).
G.f.: (2+3*x)/((1-x)*(1+2*x)).
a(n+1) - a(n) = (-1)^(n+1)*A000079(n).
a(n+1) - 2*a(n) = -a(n+2).
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MATHEMATICA
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(5+(-2)^Range[0, 30])/3 (* or *) LinearRecurrence[{-1, 2}, {2, 1}, 40] (* Harvey P. Dale, Apr 23 2019 *)
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PROG
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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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