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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

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R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973 [Cached copy, with permission]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

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)

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

Adjacent sequences:  A244863 A244864 A244865 * A244867 A244868 A244869

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Jul 07 2014

STATUS

approved

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Last modified August 13 22:57 EDT 2020. Contains 336473 sequences. (Running on oeis4.)