A244870 Number of magic labelings with magic sum n of 2nd graph shown in link.

1, 8, 37, 121, 318, 717, 1446, 2678, 4639, 7614, 11955, 18087, 26516, 37835, 52732, 71996, 96525, 127332, 165553, 212453, 269434, 338041, 419970, 517074, 631371, 765050, 920479, 1100211, 1306992, 1543767, 1813688, 2120120, 2466649, 2857088, 3295485

Offset

0,2

Links

Table of n, a(n) for n=0..34.

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R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973 [Cached copy, with permission]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 (5, -9, 5, 5, -9, 5, -1).

Formula

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

a(n) = 7*n^5/120 + 7*n^4/16 + 35*n^3/24 + 21*n^2/8 + 149*n/60 + (-1)^n/32 + 31/32. [Bruno Berselli, Jul 08 2014]

Mathematica

Table[7 n^5/120 + 7 n^4/16 + 35 n^3/24 + 21 n^2/8 + 149 n/60 + (-1)^n/32 + 31/32, {n, 0, 40}] (* Bruno Berselli, Jul 08 2014 *)

Crossrefs

Cf. A244869-A244876.

Sequence in context: A302411 A303178 A250168 * A309281 A296537 A052387

Adjacent sequences: A244867 A244868 A244869 * A244871 A244872 A244873

Keyword

nonn,easy

Author

N. J. A. Sloane, Jul 08 2014

Status

approved