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

0,2

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

Table of n, a(n) for n=0..22.

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.

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).

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].

Prog

(PARI) 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

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).

Sequence in context: A136539 A267797 A163710 * A061618 A185819 A270960

Adjacent sequences: A293307 A293308 A293309 * A293311 A293312 A293313

Keyword

nonn

Author

L. Edson Jeffery, Oct 06 2017

Status

approved