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A084172
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a(n) = 3*a(n-1) - a(n-2) - 3*a(n-3) + 2*a(n-4).
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4
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1, 2, 4, 9, 19, 40, 82, 167, 337, 678, 1360, 2725, 5455, 10916, 21838, 43683, 87373, 174754, 349516, 699041, 1398091, 2796192, 5592394, 11184799, 22369609, 44739230, 89478472, 178956957, 357913927, 715827868, 1431655750, 2863311515
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OFFSET
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0,2
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COMMENTS
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Original name was: Generalized Jacobsthal numbers.
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LINKS
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FORMULA
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a(n) = 2^(n+2)/3 - (-1)^n/12 - (2*n+1)/4.
G.f: (2*x^3 - x^2 - x + 1)/( (x+1)*(1-2*x)*(1-x)^2).
a(n+2) = a(n+1) + 2*a(n) + n, a(0)=0, a(1)=2.
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MATHEMATICA
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LinearRecurrence[{3, -1, -3, 2}, {1, 2, 4, 9}, 40] (* Harvey P. Dale, Nov 13 2013 *)
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PROG
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(Magma) [2^(n+2)/3-(-1)^n/12-(2*n+1)/4: n in [0..35]]; // Vincenzo Librandi, Jul 05 2011
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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