

A339488


a(n) = H(n1, n, n+1) where H(a, b, c) = (a + b + c)*(a + b  c)*(b + c  a)*(c + a  b) is Heron's polynomial.


1



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

0,2


COMMENTS

The term 'Heron's polynomial' is not standard but inspired by Roger Alperin's proof of Heron's formula.


REFERENCES

Reuben Hersh, Experiencing mathematics: What do we do, when we do mathematics?, p. 107, 2014.


LINKS



FORMULA

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.


MAPLE

seq(3*n^2*(n^2  4), n=0..34);


CROSSREFS



KEYWORD

sign


AUTHOR



STATUS

approved



