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

1, 76, 1460, 13604, 81555, 363606, 1310974, 4029310, 10936124, 26868719, 60843972, 128724276, 257103166, 488789593, 890341484, 1562177132, 2651877099, 4371379686, 7018869628, 11006262508, 16893296453, 25429357976, 37604290362

Offset: 0

Author

L. Edson Jeffery, Oct 06 2017

Keywords

• nonn

Comments

The graph LOOP X C_n is constructed by attaching a loop to each vertex of the cycle graph C_n.

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.

Links

• G. E. Andrews, P. Paule and A. Riese, MacMahon's partition analysis III. The Omega package.
• Eric Weisstein's World of Mathematics, Cycle Graph.
• Eric Weisstein's World of Mathematics, Graph Loop.

Crossrefs

Cf. A293311, A293312.

Cf. A000027, A000217, A019298, A006325, A244497, A244879, A244873, A244880, A293309 (magic labelings of LOOP X C_k, for k=1..8,10).

Programs

Mathematica

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]

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

Formula

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).