A244498 Number of magic labelings of the nodes of the 4 X 4 grid graph with magic sum n.

1, 36, 446, 3172, 15891, 62408, 204828, 585672, 1501269, 3521452, 7674810, 15723500, 30556903, 56739216, 101252408, 174482832, 291507177, 473741364, 751024438, 1164218484, 1768415099, 2636848984, 3865629780, 5579414360, 7938153405, 11145058236, 15455946546, 21190138876, 28743091407

Offset: 0

Author

N. J. A. Sloane, Jul 07 2014

Keywords

• nonn
• easy

Comments

The graph has 16 nodes and 24 edges.

The node labels are nonnegative integers, and the sum along any of the 4 rows or 4 columns is n.

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973 [Cached copy, with permission]
• Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Programs

PARI

Vec((1 + 26*x + 131*x^2 + 212*x^3 + 131*x^4 + 26*x^5 + x^6) / ((1 - x)^10) + O(x^40)) \\ Colin Barker, Jan 11 2017

Formula

G.f.: (1 + 26*x + 131*x^2 + 212*x^3 + 131*x^4 + 26*x^5 + x^6) / ((1 - x)^10).

From Colin Barker, Jan 11 2017: (Start)

a(n) = (7560 + 34164*n + 67044*n^2 + 75190*n^3 + 53382*n^4 + 25095*n^5 + 7896*n^6 + 1620*n^7 + 198*n^8 + 11*n^9) / 7560.

a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>9.

(End)