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Number of magic labelings of the cycle-of-loops graph LOOP X C_6 having magic sum n, where LOOP is the 1-vertex, 1-loop-edge graph.
12

%I #26 Jul 30 2019 10:27:31

%S 1,18,129,571,1884,5103,11998,25362,49347,89848,154935,255333,404950,

%T 621453,926892,1348372,1918773,2677518,3671389,4955391,6593664,

%U 8660443,11241066,14433030,18347095,23108436,28857843,35752969,43969626,53703129,65169688,78607848

%N Number of magic labelings of the cycle-of-loops graph LOOP X C_6 having magic sum n, where LOOP is the 1-vertex, 1-loop-edge graph.

%H Colin Barker, <a href="/A244879/b244879.txt">Table of n, a(n) for n = 0..1000</a>

%H R. P. Stanley, <a href="/A002721/a002721.pdf">Examples of Magic Labelings</a>, Unpublished Notes, 1973 [Cached copy, with permission]

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).

%F G.f.: (1 + 11*x + 24*x^2 + 11*x^3 + x^4) / (1 - x)^7.

%F From _Colin Barker_, Jan 11 2017: (Start)

%F a(n) = (120 + 438*n + 677*n^2 + 570*n^3 + 275*n^4 + 72*n^5 + 8*n^6) / 120.

%F a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n > 6.

%F (End)

%t CoefficientList[Series[(1 + 11 x + 24 x^2 + 11 x^3 + x^4)/(1 - x)^7, {x, 0, 31}], x] (* _Michael De Vlieger_, Sep 15 2017 *)

%t LinearRecurrence[{7,-21,35,-35,21,-7,1},{1,18,129,571,1884,5103,11998},40] (* _Harvey P. Dale_, Jul 30 2019 *)

%o (PARI) Vec((1 + 11*x + 24*x^2 + 11*x^3 + x^4) / (1 - x)^7 + O(x^40)) \\ _Colin Barker_, Jan 11 2017

%Y Cf. A019298, A006325, A244497, A292281, A244873, A244880.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Jul 08 2014

%E Name corrected by _David J. Seal_, Sep 13 2017