A244869 Number of magic labelings with magic sum n of first graph shown in link.

1, 9, 43, 143, 379, 859, 1738, 3226, 5597, 9197, 14453, 21881, 32095, 45815, 63876, 87236, 116985, 154353, 200719, 257619, 326755, 410003, 509422, 627262, 765973, 928213, 1116857, 1335005, 1585991, 1873391, 2201032, 2573000, 2993649, 3467609, 3999795, 4595415, 5259979, 5999307, 6819538

Offset: 0

Author

N. J. A. Sloane, Jul 08 2014

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• 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• R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973 [Cached copy, with permission]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).

Crossrefs

Cf. A244869-A244876.

Programs

Mathematica

LinearRecurrence[{5,-9,5,5,-9,5,-1},{1,9,43,143,379,859,1738},50] (* Paolo Xausa, Dec 06 2023 *)

PARI

Vec((1+4*x+7*x^2+4*x^3+x^4) / ((1-x)^6*(1+x)) + O(x^40)) \\ Colin Barker, Jan 11 2017

Formula

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

From Colin Barker, Jan 11 2017: (Start)

a(n) = (15*(63 + (-1)^n) + 2592*n + 2880*n^2 + 1660*n^3 + 510*n^4 + 68*n^5) / 960.

a(n) = 5*a(n-1) - 9*a(n-2) + 5*a(n-3) + 5*a(n-4) - 9*a(n-5) + 5*a(n-6) - a(n-7) for n>6.

(End)