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A244874
Number of magic labelings with magic sum n of 6th graph shown in link.
2
1, 17, 137, 707, 2709, 8417, 22408, 53008, 114251, 228431, 429325, 766167, 1308451, 2151643, 3423880, 5293736, 7979133, 11757477, 16977097, 24070067, 33566489, 46110317, 62476800, 83591624, 110551831, 144648595, 187391933, 240537431, 306115063, 386460183, 484246768
OFFSET
0,2
LINKS
R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973 [Cached copy, with permission]
Index entries for linear recurrences with constant coefficients, signature (7,-20,28,-14,-14,28,-20,7,-1).
FORMULA
G.f.: (1 + 10*x + 38*x^2 + 60*x^3 + 38*x^4 + 10*x^5 + x^6) / ((1 - x)^8*(1 + x)).
a(n) = (-315*(-129+(-1)^n) + 138528*n + 202104*n^2 + 171248*n^3 + 93030*n^4 + 32312*n^5 + 6636*n^6 + 632*n^7) / 40320. - Colin Barker, Jan 11 2017
MATHEMATICA
LinearRecurrence[{7, -20, 28, -14, -14, 28, -20, 7, -1}, {1, 17, 137, 707, 2709, 8417, 22408, 53008, 114251}, 40] (* Harvey P. Dale, Jun 30 2022 *)
PROG
(PARI) Vec((1 + 10*x + 38*x^2 + 60*x^3 + 38*x^4 + 10*x^5 + x^6) / ((1 - x)^8*(1 + x)) + O(x^40)) \\ Colin Barker, Jan 11 2017
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jul 08 2014
STATUS
approved