A244866 Let G denote the 7-node, 12-edge graph formed from a hexagon with main diagonals drawn and a node at the center; a(n) = number of magic labelings of G with magic sum 2n.
1, 18, 114, 438, 1263, 3024, 6356, 12132, 21501, 35926, 57222, 87594, 129675, 186564, 261864, 359720, 484857, 642618, 839002, 1080702, 1375143, 1730520, 2155836, 2660940, 3256565, 3954366, 4766958, 5707954, 6792003, 8034828, 9453264, 11065296, 12890097, 14948066, 17260866, 19851462, 22744159
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- R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973 [Cached copy, with permission]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 (6,-15,20,-15,6,-1).
Programs
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Mathematica
LinearRecurrence[{6,-15,20,-15,6,-1},{1,18,114,438,1263,3024},40] (* Harvey P. Dale, Nov 09 2022 *) -
PARI
Vec((1 + 12*x + 21*x^2 + 4*x^3) / (1 - x)^6 + O(x^40)) \\ Colin Barker, Jan 11 2017
Formula
G.f.: (1 + 12*x + 21*x^2 + 4*x^3) / (1 - x)^6.
From Colin Barker, Jan 11 2017: (Start)
a(n) = (n + 1)*(n + 2)*(19*n^3 + 63*n^2 + 68*n + 30) / 60.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>5.
(End)