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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
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973 [Cached copy, with permission]
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)
MATHEMATICA
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1, 18, 114, 438, 1263, 3024}, 40] (* Harvey P. Dale, Nov 09 2022 *)
PROG
(PARI) Vec((1 + 12*x + 21*x^2 + 4*x^3) / (1 - x)^6 + O(x^40)) \\ Colin Barker, Jan 11 2017
CROSSREFS
Sequence in context: A160765 A192511 A324623 * A125328 A126486 A251937
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jul 07 2014
STATUS
approved

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Last modified July 13 21:44 EDT 2024. Contains 374288 sequences. (Running on oeis4.)