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A161712
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a(n) = (4*n^3 - 6*n^2 + 8*n + 3)/3.
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17
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1, 3, 9, 27, 65, 131, 233, 379, 577, 835, 1161, 1563, 2049, 2627, 3305, 4091, 4993, 6019, 7177, 8475, 9921, 11523, 13289, 15227, 17345, 19651, 22153, 24859, 27777, 30915, 34281, 37883, 41729, 45827, 50185, 54811, 59713, 64899, 70377, 76155
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OFFSET
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0,2
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COMMENTS
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{a(k): 0 <= k < 4} = divisors of 27:
a(n), n > 0 is the number of points of the half-integer lattice in R^n that lie in the open unit ball. - Tom Harris, Jun 15 2021
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LINKS
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FORMULA
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a(n) = C(n,0) + 2*C(n,1) + 4*C(n,2) + 8*C(n,3).
E.g.f.: (1/3)*(4*x^3 + 6*x^2 + 6*x + 3)*exp(x). - G. C. Greubel, Jul 16 2017
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EXAMPLE
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Differences of divisors of 27 to compute the coefficients of their interpolating polynomial, see formula:
1 3 9 27
2 6 18
4 12
8
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MATHEMATICA
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Table[(4n^3-6n^2+8n+3)/3, {n, 0, 80}] (* Harvey P. Dale, Apr 13 2011 *)
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PROG
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(Magma) [(4*n^3 - 6*n^2 + 8*n + 3)/3: n in [0..40]]; // Vincenzo Librandi, Jul 17 2011
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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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