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A339488
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a(n) = H(n-1, n, n+1) where H(a, b, c) = (a + b + c)*(a + b - c)*(b + c - a)*(c + a - b) is Heron's polynomial.
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1
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0, -9, 0, 135, 576, 1575, 3456, 6615, 11520, 18711, 28800, 42471, 60480, 83655, 112896, 149175, 193536, 247095, 311040, 386631, 475200, 578151, 696960, 833175, 988416, 1164375, 1362816, 1585575, 1834560, 2111751, 2419200, 2759031, 3133440, 3544695, 3995136
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OFFSET
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0,2
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COMMENTS
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The term 'Heron's polynomial' is not standard but inspired by Roger Alperin's proof of Heron's formula.
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REFERENCES
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Reuben Hersh, Experiencing mathematics: What do we do, when we do mathematics?, p. 107, 2014.
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LINKS
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FORMULA
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a(n) = 3*n^4 - 12*n^2.
a(n) = [x^n] 9*x*(x + 1)*(x^2 - 6*x + 1)/(x - 1)^5.
a(2*n)/(24)^2 = binomial(n^2, 2)/6 = A002415(n) for n >= 0.
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MAPLE
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seq(3*n^2*(n^2 - 4), n=0..34);
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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