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%I #12 Mar 07 2021 18:57:58
%S 12,23,37,54,74,97,123,152,184,219,257,298,342,389,439,492,548,607,
%T 669,734,802,873,947,1024,1104,1187,1273,1362,1454,1549,1647,1748,
%U 1852,1959,2069,2182,2298,2417,2539,2664,2792,2923,3057,3194,3334,3477,3623,3772,3924
%N a(n) is the maximum value of the magic constant in a normal magic triangle of order n.
%H Terrel Trotter, <a href="http://www.teherba.org/trottermath.net/simpleops/magictri.html">Normal Magic Triangles of Order n</a>, Journal of Recreational Mathematics Vol. 5, No. 1, 1972, pp. 28-32.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F O.g.f.: x^3*(12 - 13*x + 4*x^2))/(1 - x)^3.
%F E.g.f.: 3 + x - 2*x^2 - exp(x)*(6 - 4*x - 3*x^2)/2.
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 5.
%F a(n) = (3*n^2 + n - 6)/2 for n > 2.
%F a(n) = A285009(n) + A016777(n-2) - 1 for n > 3.
%F a(n) = A095794(n) - 2 = A140090(n-1) - 1. - _Hugo Pfoertner_, Feb 18 2021
%t LinearRecurrence[{3,-3,1},{12,23,37},49]
%Y Cf. A005449, A016777, A095794, A130808, A140090, A179805, A285009.
%K nonn,easy
%O 3,1
%A _Stefano Spezia_, Feb 18 2021
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