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 A293309 #21 Aug 08 2025 05:53:59
%S A293309 1,123,3281,39175,286555,1508401,6271378,21836366,66220705,179784715,
%T A293309 445824731,1025102013,2211041131,4514532465,8789910980,16416797116,
%U A293309 29556115153,51502789451,87162399205,143684487475,231291309931,364347612673,562724586326
%N A293309 Number of magic labelings of the graph LOOP X C_10 (see comments) having magic sum n, n >= 0.
%C A293309 The graph LOOP X C_n is constructed by attaching a loop to each vertex of the cycle graph C_n.
%C A293309 The generating function for this sequence was found via the "Omega" package for Mathematica authored by Axel Riese. The package can be downloaded from the link given in the article by G. E. Andrews et al.
%H A293309 G. E. Andrews, P. Paule and A. Riese, <a href="http://www.risc.uni-linz.ac.at/research/combinat/risc/publications/#ppaule">MacMahon's partition analysis III. The Omega package</a>.
%H A293309 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CycleGraph.html">Cycle Graph</a>.
%H A293309 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Graph Loop.html">Graph Loop</a>.
%H A293309 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
%F A293309 G.f.: (1 + 112*z + 1983*z^2 + 9684*z^3 + 16120*z^4 + 9684*z^5 + 1983*z^6 + 112*z^7 + z^8)/(1 - z)^11.
%t A293309 CoefficientList[Series[(1 + 112*z + 1983*z^2 + 9684*z^3 + 16120*z^4 + 9684*z^5 + 1983*z^6 + 112*z^7 + z^8)/(1 - z)^11, {z, 0, 22}], z]
%t A293309 LinearRecurrence[{11, -55, 165, -330, 462, -462, 330, -165, 55, -11, 1}, {1, 123, 3281, 39175, 286555, 1508401, 6271378, 21836366, 66220705, 179784715, 445824731}, 25] (* _Vincenzo Librandi_, Oct 12 2017 *)
%Y A293309 Cf. A293311, A293312.
%Y A293309 Cf. A000027, A000217, A019298, A006325, A244497, A244879, A244873, A244880, A293310 (magic labelings of LOOP X C_k, for k=1..9).
%K A293309 nonn
%O A293309 0,2
%A A293309 _L. Edson Jeffery_, Oct 05 2017