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

%I A244498 #12 Nov 10 2024 02:24:16
%S A244498 1,36,446,3172,15891,62408,204828,585672,1501269,3521452,7674810,
%T A244498 15723500,30556903,56739216,101252408,174482832,291507177,473741364,
%U A244498 751024438,1164218484,1768415099,2636848984,3865629780,5579414360,7938153405,11145058236,15455946546,21190138876,28743091407
%N A244498 Number of magic labelings of the nodes of the 4 X 4 grid graph with magic sum n.
%C A244498 The graph has 16 nodes and 24 edges.
%C A244498 The node labels are nonnegative integers, and the sum along any of the 4 rows or 4 columns is n.
%H A244498 Colin Barker, <a href="/A244498/b244498.txt">Table of n, a(n) for n = 0..1000</a>
%H A244498 R. P. Stanley, <a href="/A002721/a002721.pdf">Examples of Magic Labelings</a>, Unpublished Notes, 1973 [Cached copy, with permission]
%H A244498 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
%F A244498 G.f.: (1 + 26*x + 131*x^2 + 212*x^3 + 131*x^4 + 26*x^5 + x^6) / ((1 - x)^10).
%F A244498 From _Colin Barker_, Jan 11 2017: (Start)
%F A244498 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.
%F A244498 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.
%F A244498 (End)
%o A244498 (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
%K A244498 nonn,easy
%O A244498 0,2
%A A244498 _N. J. A. Sloane_, Jul 07 2014