A244873 Number of magic labelings of the prism graph I X C_7 with magic sum n.

1, 29, 289, 1640, 6604, 21122, 57271, 137155, 298184, 599954, 1132942, 2029229, 3475465, 5728289, 9132418, 14141618, 21342771, 31483251, 45501823, 64563278, 90097018, 123839804, 167882881, 224723693, 297322402, 389163424, 504322196, 647537387, 824288767, 1040880947, 1304533204

Offset

0,2

Comments

The graph is the 5th one shown in the link. This sequence is also the number of magic labelings of the cycle-of-loops graph LOOP X C_7 with magic sum n, where LOOP is the 1-vertex, 1-loop-edge graph. A similar identity holds between the sequences for I X C_k and LOOP X C_k for all odd k. - David J. Seal, Sep 14 2017

Links

Table of n, a(n) for n=0..30.

N. J. A. Sloane, Graphs for A244869-A244876.

R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973 [Cached copy, with permission]

Index entries for linear recurrences with constant coefficients, signature (7, -20, 28, -14, -14, 28, -20, 7, -1).

Formula

G.f.: (1+22*x+106*x^2+169*x^3+106*x^4+22*x^5+x^6)/((1-x)^8*(1+x)).

a(n) = 61*n^7/1440 + 427*n^6/960 + 1463*n^5/720 + 2009*n^4/384 + 11809*n^3/1440 + 1253*n^2/160 + 169*n/40 + (-1)^n/256 + 255/256. [Bruno Berselli, Jul 08 2014]

Mathematica

Table[61 n^7/1440 + 427 n^6/960 + 1463 n^5/720 + 2009 n^4/384 + 11809 n^3/1440 + 1253 n^2/160 + 169 n/40 + (-1)^n/256 + 255/256, {n, 0, 30}] (* Bruno Berselli, Jul 08 2014 *)
LinearRecurrence[{7, -20, 28, -14, -14, 28, -20, 7, -1}, {1, 29, 289, 1640, 6604, 21122, 57271, 137155, 298184}, 40] (* Harvey P. Dale, Aug 09 2017 *)

Crossrefs

Cf. A244869-A244876.

Cf. A019298, A061927, A244497, A292281, A289992 (analogs for prism graphs I X C_k, k = 3,4,5,6,8).

Cf. A006325, A244879, A244880 (analogs for LOOP X C_k, k = 4,6,8).

Sequence in context: A124310 A101380 A264298 * A125392 A126550 A146015

Adjacent sequences: A244870 A244871 A244872 * A244874 A244875 A244876

Keyword

nonn,easy

Author

N. J. A. Sloane, Jul 08 2014

Extensions

Name made more self-contained by David J. Seal, Sep 14 2017

Status

approved