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A168233
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a(n) = 3*n - a(n-1) - 1 for n>0, a(1)=1.
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5
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1, 4, 4, 7, 7, 10, 10, 13, 13, 16, 16, 19, 19, 22, 22, 25, 25, 28, 28, 31, 31, 34, 34, 37, 37, 40, 40, 43, 43, 46, 46, 49, 49, 52, 52, 55, 55, 58, 58, 61, 61, 64, 64, 67, 67, 70, 70, 73, 73, 76, 76, 79, 79, 82, 82, 85, 85, 88, 88, 91, 91, 94, 94, 97, 97, 100, 100, 103, 103, 106
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = (6*n + 3*(-1)^n + 1)/4.
G.f.: x*(1 + 3*x - x^2)/((1+x)*(1-x)^2).
a(n) = a(n-1) + a(n-2) - a(n-3), for n>3.
a(n) + a(n-1) = A016789(n-1) for n>1.
E.g.f.: (1/4)*(3 - 4*exp(x) + (1 + 6*x)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 16 2016
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MAPLE
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MATHEMATICA
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CoefficientList[Series[(1 + 3*x - x^2)/((1+x) * (1-x)^2), {x, 0, 100}], x] (* Vincenzo Librandi, Feb 02 2013 *)
LinearRecurrence[{1, 1, -1}, {1, 4, 4}, 80] (* Harvey P. Dale, Oct 13 2015 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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