A292281 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

Table of n, a(n) for n=0..30.

R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973.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).

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]

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 *)

CROSSREFS

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

Sequence in context: A056114 A281204 A186259 * A056932 A304508 A010826

Adjacent sequences: A292278 A292279 A292280 * A292282 A292283 A292284

KEYWORD

nonn,easy

AUTHOR

David J. Seal, Sep 13 2017

STATUS

approved