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A244876
Number of magic labelings with magic sum n of 8th graph shown in link.
8
1, 18, 154, 813, 3157, 9880, 26429, 62713, 135470, 271285, 510485, 911840, 1558368, 2564093, 4082142, 6313934, 9519951, 14031732, 20265700, 28738335, 40083439, 55070862, 74627587, 99860383, 132081092, 172833583, 223923623, 287450506, 365841890, 461890475, 578794188
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R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973 [Cached copy, with permission]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 (5, -7, -5, 22, -14, -14, 22, -5, -7, 5, -1).
FORMULA
G.f.: (1+13*x+71*x^2+174*x^3+238*x^4+174*x^5+71*x^6+13*x^7+x^8)/((1-x)^8*(1+x)^3).
a(n) = 3*n^7/160 + 63*n^6/320 + 151*n^5/160 + 339*n^4/128 + 2251*n^3/480 + n^2*(-1)^n/64 + 1677*n^2/320 + 3*n*(-1)^n/64 + 3259*n/960 + 9*(-1)^n/256 + 247/256. [Bruno Berselli, Jul 08 2014]
MATHEMATICA
Table[3 n^7/160 + 63 n^6/320 + 151 n^5/160 + 339 n^4/128 + 2251 n^3/480 + n^2 (-1)^n/64 + 1677 n^2/320 + 3 n (-1)^n/64 + 3259 n/960 + 9 (-1)^n/256 + 247/256, {n, 0, 30}] (* Bruno Berselli, Jul 08 2014 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jul 08 2014
STATUS
approved