cp's OEIS Frontend

A293310 Number of magic labelings of the graph LOOP X C_9 (see comments) having magic sum n, n >= 0.

%I A293310 #17 Aug 08 2025 05:54:19
%S A293310 1,76,1460,13604,81555,363606,1310974,4029310,10936124,26868719,
%T A293310 60843972,128724276,257103166,488789593,890341484,1562177132,
%U A293310 2651877099,4371379686,7018869628,11006262508,16893296453,25429357976,37604290362
%N A293310 Number of magic labelings of the graph LOOP X C_9 (see comments) having magic sum n, n >= 0.
%C A293310 The graph LOOP X C_n is constructed by attaching a loop to each vertex of the cycle graph C_n.
%C A293310 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 A293310 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 A293310 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CycleGraph.html">Cycle Graph</a>.
%H A293310 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Graph Loop.html">Graph Loop</a>.
%F A293310 G.f.: (1 + 67*z + 811*z^2 + 3049*z^3 + 4609*z^4 + 3049*z^5 + 811*z^6 + 67*z^7 + z^8)/((1 + z)*(1 - z)^10).
%t A293310 CoefficientList[Series[(1 + 67*z + 811*z^2 + 3049*z^3 + 4609*z^4 + 3049*z^5 + 811*z^6 + 67*z^7 + z^8)/((1 + z)*(1 - z)^10), {z, 0, 22}], z]
%o A293310 (PARI) my(x='x+O('x^99));Vec((1+67*x+811*x^2+3049*x^3+4609*x^4+3049*x^5+811*x^6+67*x^7+x^8)/((1+x)*(1-x)^10)) \\ _Altug Alkan_, Oct 11 2017
%Y A293310 Cf. A293311, A293312.
%Y A293310 Cf. A000027, A000217, A019298, A006325, A244497, A244879, A244873, A244880, A293309 (magic labelings of LOOP X C_k, for k=1..8,10).
%K A293310 nonn
%O A293310 0,2
%A A293310 _L. Edson Jeffery_, Oct 06 2017