A293309 Number of magic labelings of the graph LOOP X C_10 (see comments) having magic sum n, n >= 0.

1, 123, 3281, 39175, 286555, 1508401, 6271378, 21836366, 66220705, 179784715, 445824731, 1025102013, 2211041131, 4514532465, 8789910980, 16416797116, 29556115153, 51502789451, 87162399205, 143684487475, 231291309931, 364347612673, 562724586326

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.

Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Formula

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.

Mathematica

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].
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 *)

Crossrefs

Cf. A293311, A293312.

Cf. A000027, A000217, A019298, A006325, A244497, A244879, A244873, A244880, A293310 (magic labelings of LOOP X C_k, for k=1..9).

Sequence in context: A160040 A297524 A163711 * A297754 A068239 A098683

Adjacent sequences: A293306 A293307 A293308 * A293310 A293311 A293312

Keyword

nonn

Author

L. Edson Jeffery, Oct 05 2017

Status

approved