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

0,2

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R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973 [Cached copy, with permission]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).

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)

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 *)

Prog

(PARI) Vec((1 + 11*x + 24*x^2 + 11*x^3 + x^4) / (1 - x)^7 + O(x^40)) \\ Colin Barker, Jan 11 2017

Crossrefs

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

Sequence in context: A335781 A041620 A375329 * A142965 A298275 A299137

Adjacent sequences: A244876 A244877 A244878 * A244880 A244881 A244882

Keyword

nonn,easy

Author

N. J. A. Sloane, Jul 08 2014

Extensions

Name corrected by David J. Seal, Sep 13 2017

Status

approved