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

0,2

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R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973 [Cached copy, with permission]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

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 *)

Crossrefs

Cf. A244869-A244876.

Sequence in context: A233326 A092317 A160075 * A293875 A044347 A113527

Adjacent sequences: A244869 A244870 A244871 * A244873 A244874 A244875

Keyword

nonn,easy

Author

N. J. A. Sloane, Jul 08 2014

Status

approved