A341740 a(n) is the maximum value of the magic constant in a normal magic triangle of order n.

12, 23, 37, 54, 74, 97, 123, 152, 184, 219, 257, 298, 342, 389, 439, 492, 548, 607, 669, 734, 802, 873, 947, 1024, 1104, 1187, 1273, 1362, 1454, 1549, 1647, 1748, 1852, 1959, 2069, 2182, 2298, 2417, 2539, 2664, 2792, 2923, 3057, 3194, 3334, 3477, 3623, 3772, 3924

Offset: 3

Author

Stefano Spezia, Feb 18 2021

Keywords

• nonn
• easy

Links

• Terrel Trotter, Normal Magic Triangles of Order n, Journal of Recreational Mathematics Vol. 5, No. 1, 1972, pp. 28-32.
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A005449, A016777, A095794, A130808, A140090, A179805, A285009.

Programs

Mathematica

LinearRecurrence[{3,-3,1},{12,23,37},49]

Formula

O.g.f.: x^3*(12 - 13*x + 4*x^2)/(1 - x)^3.

E.g.f.: 3 + x - 2*x^2 - exp(x)*(6 - 4*x - 3*x^2)/2.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 5.

a(n) = (3*n^2 + n - 6)/2 for n > 2.

a(n) = A285009(n) + A016777(n-2) - 1 for n > 3.

a(n) = A095794(n) - 2 = A140090(n-1) - 1. - Hugo Pfoertner, Feb 18 2021