A244879 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.
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
Offset: 0
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- R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973 [Cached copy, with permission]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 (7,-21,35,-35,21,-7,1).
Programs
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Mathematica
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 *) -
PARI
Vec((1 + 11*x + 24*x^2 + 11*x^3 + x^4) / (1 - x)^7 + O(x^40)) \\ Colin Barker, Jan 11 2017
Formula
G.f.: (1 + 11*x + 24*x^2 + 11*x^3 + x^4) / (1 - x)^7.
From Colin Barker, Jan 11 2017: (Start)
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)
Extensions
Name corrected by David J. Seal, Sep 13 2017