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A244498
Number of magic labelings of the nodes of the 4 X 4 grid graph with magic sum n.
1
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
0,2
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
R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973 [Cached copy, with permission]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).
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)
PROG
(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
CROSSREFS
Sequence in context: A222781 A281403 A256149 * A110693 A104671 A323549
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jul 07 2014
STATUS
approved