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

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• R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973 [Cached copy, with permission]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

Crossrefs

Cf. A244869-A244876.

Programs

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 *)

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]