A244872 Number of magic labelings with magic sum n of 4th graph shown in link.

1, 15, 114, 569, 2138, 6562, 17329, 40765, 87512, 174452, 327137, 582784, 993895, 1632561, 2595510, 4009958, 6040323, 8895861, 12839284, 18196419, 25366968, 34836428, 47189231, 63123163, 83465122, 109188274, 141430667, 181515362, 230972141, 291560851, 365296444

Offset: 0

Author

N. J. A. Sloane, Jul 08 2014

Keywords

• nonn
• easy

Links

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• R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973 [Cached copy, with permission]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

Crossrefs

Cf. A244869-A244876.

Programs

Mathematica

Table[17 n^7/1440 + 119 n^6/960 + 28 n^5/45 + 721 n^4/384 + 5243 n^3/1440 + 721 n^2/160 + 129 n/40 + (-1)^n/256 + 255/256, {n, 0, 30}]
LinearRecurrence[{7,-20,28,-14,-14,28,-20,7,-1},{1,15,114,569,2138,6562,17329,40765,87512},40] (* Harvey P. Dale, Nov 01 2021 *)

Formula

G.f.: (1+8*x+29*x^2+43*x^3+29*x^4+8*x^5+x^6)/((1-x)^8*(1+x)).

a(n) = 17*n^7/1440 + 119*n^6/960 + 28*n^5/45 + 721*n^4/384 + 5243*n^3/1440 + 721*n^2/160 + 129*n/40 + (-1)^n/256 + 255/256. [Bruno Berselli, Jul 08 2014]