A292281 Number of magic labelings of the prism graph I X C_6 having magic sum n.

1, 20, 167, 867, 3322, 10309, 27410, 64770, 139479, 278674, 523457, 933725, 1594008, 2620411, 4168756, 6444020, 9711165, 14307456, 20656363, 29283143, 40832198, 56086305, 75987814, 101661910, 134442035, 175897566, 227863845, 292474657, 372197252, 469870007, 588742824

Offset: 0

Author

David J. Seal, Sep 13 2017

Keywords

• nonn
• easy

Links

• R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973. [Cached copy, with permission]
• Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Crossrefs

Cf. A019298, A061927, A244497, A244879, A244873, A289992.

Programs

Mathematica

f[n_] := SeriesCoefficient[(1 + 11 x + 24 x^2 + 11 x^3 + x^4)/(1 - x)^7, {x, 0, n}]; Table[f[n] + 2 Sum[f[i], {i, 0, n - 1}], {n, 0, 24}] (* Michael De Vlieger, Sep 15 2017 *)

Formula

a(n) = A244879(n) + 2*Sum_{i=0..n-1} A244879(i).

From Colin Barker, Sep 13 2017: (Start)

G.f.: (1 + x)*(1 + 11*x + 24*x^2 + 11*x^3 + x^4) / (1 - x)^8.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>7.

(End)

[Proof of the g.f. follows from the g.f. of A244879 with the resummation demonstrated in A289992: g.f. = A244879(x)*(1+2*x/(1-x)). - R. J. Mathar, Mar 09 2025]