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A084672
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Expansion of g.f.: (1+x^2+2*x^4)/((1-x^3)*(1-x)^2).
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1
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1, 2, 4, 7, 12, 18, 25, 34, 44, 55, 68, 82, 97, 114, 132, 151, 172, 194, 217, 242, 268, 295, 324, 354, 385, 418, 452, 487, 524, 562, 601, 642, 684, 727, 772, 818, 865, 914, 964, 1015, 1068, 1122, 1177, 1234, 1292, 1351, 1412, 1474, 1537, 1602, 1668, 1735, 1804, 1874
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = (1/3)*(2*n^2 - n + 3 + 2*floor((n+2)/3) + floor((n+1)/3)).
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MATHEMATICA
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CoefficientList[Series[(1+x^2+2x^4)/((1-x^3)(1-x)^2), {x, 0, 70}], x] (* Harvey P. Dale, Mar 31 2011 *)
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PROG
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(Magma) [(2*n^2 -n +3 +2*Floor((n+2)/3) +Floor((n+1)/3))/3: n in [0..60]]; // G. C. Greubel, Mar 22 2023
(SageMath) [(2*n^2 -n +3 +2*((n+2)//3) +((n+1)//3))/3 for n in range(61)] # G. C. Greubel, Mar 22 2023
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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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