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A244879
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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.
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12
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1, 18, 129, 571, 1884, 5103, 11998, 25362, 49347, 89848, 154935, 255333, 404950, 621453, 926892, 1348372, 1918773, 2677518, 3671389, 4955391, 6593664, 8660443, 11241066, 14433030, 18347095, 23108436, 28857843, 35752969, 43969626, 53703129, 65169688, 78607848
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: (1 + 11*x + 24*x^2 + 11*x^3 + x^4) / (1 - x)^7.
a(n) = (120 + 438*n + 677*n^2 + 570*n^3 + 275*n^4 + 72*n^5 + 8*n^6) / 120.
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.
(End)
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MATHEMATICA
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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 *)
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {1, 18, 129, 571, 1884, 5103, 11998}, 40] (* Harvey P. Dale, Jul 30 2019 *)
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PROG
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(PARI) Vec((1 + 11*x + 24*x^2 + 11*x^3 + x^4) / (1 - x)^7 + O(x^40)) \\ Colin Barker, Jan 11 2017
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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