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A171382
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(2*2^n+7*(-1)^n)/3.
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2
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3, -1, 5, 3, 13, 19, 45, 83, 173, 339, 685, 1363, 2733, 5459, 10925, 21843, 43693, 87379, 174765, 349523, 699053, 1398099, 2796205, 5592403, 11184813, 22369619, 44739245, 89478483, 178956973, 357913939, 715827885, 1431655763, 2863311533
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OFFSET
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0,1
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COMMENTS
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a(n) = A155980(n+2).
a(n) = A135351(n+3)-A135351(n+2).
Second binomial transform of a signed version of A005032 preceded by 3.
Inverse binomial transform of A008776 preceded by 3.
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LINKS
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Table of n, a(n) for n=0..32.
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FORMULA
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a(n) = a(n-1)+2*a(n-2) for n > 1; a(0) = 3, a(1) = -1.
a(n) = 2^n-a(n-1) for n > 0; a(0) = 3.
G.f.: (3-4*x)/((1+x)*(1-2*x)).
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MATHEMATICA
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Nest[Append[#, Last[#]+2#[[-2]]]&, {3, -1}, 40] (* Harvey P. Dale, Apr 07 2011 *)
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PROG
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(MAGMA) [ (2*2^n+7*(-1)^n)/3: n in [0..32] ];
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CROSSREFS
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Cf. A155980 (First differences of A135351), A135351 ((2^n+3-7*(-1)^n+3*0^n)/6), A005032 (7*3^n), A008776 (2*3^n).
Sequence in context: A290212 A289891 A289094 * A002323 A294640 A200920
Adjacent sequences: A171379 A171380 A171381 * A171383 A171384 A171385
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KEYWORD
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sign
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AUTHOR
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Klaus Brockhaus, Dec 07 2009
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STATUS
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approved
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