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a(n) = 9*n^3/2 - 21*n^2/2 + 8*n - 4.
1

%I #22 Oct 23 2024 14:40:08

%S 6,47,148,336,638,1081,1692,2498,3526,4803,6356,8212,10398,12941,

%T 15868,19206,22982,27223,31956,37208,43006,49377,56348,63946,72198,

%U 81131,90772,101148,112286,124213,136956,150542,164998,180351,196628,213856,232062,251273

%N a(n) = 9*n^3/2 - 21*n^2/2 + 8*n - 4.

%H Bruno Berselli, <a href="/A232495/b232495.txt">Table of n, a(n) for n = 2..1000</a>

%H Jan Draisma, Emil Horobeţ, Giorgio Ottaviani, Bernd Sturmfels, and Rekha R. Thomas, <a href="https://doi.org/10.1007/s10208-014-9240-x">The Euclidean distance degree of an algebraic variety</a>, Foundations of computational mathematics, Vol. 16 (2016), pp. 99-149; <a href="http://arxiv.org/abs/1309.0049">arXiv preprint</a>, arXiv:1309.0049 [math.AG], 2013-2014. See Conjecture 3.4.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

%F G.f.: x^2*(6 + 23*x - 4*x^2 + 2*x^3) / (1 - x)^4. - _Bruno Berselli_, Dec 03 2013

%t Table[9 n^3/2 - 21 n^2/2 + 8 n - 4, {n, 2, 40}] (* _Bruno Berselli_, Dec 03 2013 *)

%t LinearRecurrence[{4,-6,4,-1},{6,47,148,336},40] (* _Harvey P. Dale_, Aug 03 2020 *)

%o (Magma) [9*n^3/2-21*n^2/2+8*n-4: n in [2..40]]; // _Bruno Berselli_, Dec 03 2013

%K nonn,easy

%O 2,1

%A _N. J. A. Sloane_, Dec 03 2013