A244871 Number of magic labelings with magic sum n of 3rd graph shown in link.

1, 10, 55, 217, 672, 1755, 4030, 8386, 16135, 29140, 49941, 81915, 129430, 198037, 294652, 427780, 607725, 846846, 1159795, 1563805, 2078956, 2728495, 3539130, 4541382, 5769907, 7263880, 9067345, 11229631, 13805730, 16856745, 20450296, 24661000, 29570905

Offset

0,2

Links

Table of n, a(n) for n=0..32.

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R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973 [Cached copy, with permission]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, -8, 0, 14, -14, 0, 8, -5, 1).

Formula

G.f.: (1+5*x+13*x^2+22*x^3+13*x^4+5*x^5+x^6)/((1-x)^7*(1+x)^2).

a(n) = n^6/48 + 3*n^5/16 + 77*n^4/96 + 2*n^3 + 37*n^2/12 - n*(-1)^n/32 + 89*n/32 - 3*(-1)^n/64 + 67/64. [Bruno Berselli, Jul 08 2014]

Mathematica

Table[n^6/48 + 3 n^5/16 + 77 n^4/96 + 2 n^3 + 37 n^2/12 - n (-1)^n/32 + 89 n/32 - 3 (-1)^n/64 + 67/64, {n, 0, 40}] (* Bruno Berselli, Jul 08 2014 *)

Crossrefs

Cf. A244869-A244876.

Sequence in context: A357730 A341989 A341070 * A162617 A341139 A070212

Adjacent sequences: A244868 A244869 A244870 * A244872 A244873 A244874

Keyword

nonn,easy

Author

N. J. A. Sloane, Jul 08 2014

Status

approved