A292281 - OEIS

%I #22 Sep 19 2017 10:48:40

%S 1,20,167,867,3322,10309,27410,64770,139479,278674,523457,933725,

%T 1594008,2620411,4168756,6444020,9711165,14307456,20656363,29283143,

%U 40832198,56086305,75987814,101661910,134442035,175897566,227863845,292474657,372197252,469870007,588742824

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

%H R. P. Stanley, <a href="/A002721/a002721.pdf">Examples of Magic Labelings</a>, Unpublished Notes, 1973 [Cached copy, with permission]

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

%F Conjectures from _Colin Barker_, Sep 13 2017: (Start)

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

%F 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.

%F (End)

%t 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 *)

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

%K nonn

%O 0,2

%A _David J. Seal_, Sep 13 2017