This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A289992 #40 Mar 10 2025 05:02:04
%S A289992 1,49,746,6122,34067,144963,506772,1524628,4074949,9898229,22220990,
%T A289992 46695870,92769495,175610631,318756136,557659432,944355593,1553488697,
%U A289992 2489980818,3898657938,5976186139,8985711691,13274641084,19296041660,27634190285
%N A289992 Number of magic labelings of the prism graph I X C_8 having magic sum n.
%H A289992 R. P. Stanley, <a href="/A002721/a002721.pdf">Examples of Magic Labelings</a>, Unpublished Notes, 1973. [Cached copy, with permission]
%H A289992 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
%F A289992 a(n) = A244880(n) + 2*Sum_{i=0..n-1} A244880(i).
%F A289992 From _Colin Barker_, Sep 13 2017: (Start)
%F A289992 G.f.: (1 + x)*(1 + 6*x + x^2)*(1 + 32*x + 70*x^2 + 32*x^3 + x^4) / (1 - x)^10.
%F A289992 a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>9. (End)
%F A289992 [Proof of the g.f. follows from the convolution formula and insertion of the g.f. A244880(x): Sum_{n>=0} a(n)x^n = Sum_{n>=0} A244880(n)*x^n +2*Sum_{n>=0} Sum_{i=0..n-1} A244880(i)*x^n = A244880(x) +2*Sum_{i>=0} Sum_{n>=i+1} A244880(i)*x^n = A244880(x) +2*Sum_{i>=0} A244880(i)*x^(i+1) Sum_{n>=0} x^n = A244880(x)+2*A244880(x)*x/(1+x) = A244880(x)*(1+2*x/(1-x)). _R. J. Mathar_, Mar 09 2025]
%Y A289992 Cf. A019298, A061927, A244497, A292281, A244873, A244880.
%K A289992 nonn,easy
%O A289992 0,2
%A A289992 _David J. Seal_, Sep 13 2017