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Number of magic labelings of the prism graph I X C_7 with magic sum n.
14

%I #21 Sep 19 2017 12:22:23

%S 1,29,289,1640,6604,21122,57271,137155,298184,599954,1132942,2029229,

%T 3475465,5728289,9132418,14141618,21342771,31483251,45501823,64563278,

%U 90097018,123839804,167882881,224723693,297322402,389163424,504322196,647537387,824288767,1040880947,1304533204

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

%C 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

%H N. J. A. Sloane, <a href="/A244869/a244869.jpg">Graphs for A244869-A244876.</a>

%H R. P. Stanley, <a href="/A002721/a002721.pdf">Examples of Magic Labelings</a>, Unpublished Notes, 1973 [Cached copy, with permission]

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (7, -20, 28, -14, -14, 28, -20, 7, -1).

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

%F 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]

%t 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 *)

%t 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 *)

%Y Cf. A244869-A244876.

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

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

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Jul 08 2014

%E Name made more self-contained by _David J. Seal_, Sep 14 2017