A008421 Crystal ball sequence for 10-dimensional cubic lattice.
1, 21, 221, 1561, 8361, 36365, 134245, 433905, 1256465, 3317445, 8097453, 18474633, 39753273, 81270333, 158819253, 298199265, 540279585, 948062325, 1616336765, 2684641785, 4354393801, 6911195501, 10753517061, 16429137361, 24680949041, 36503969061
Offset: 0
Links
- T. D. Noe, Table of n, a(n) for n = 0..1000
- J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).
- Index entries for crystal ball sequences
- Index entries for linear recurrences with constant coefficients, signature (11, -55, 165, -330, 462, -462, 330, -165, 55, -11, 1).
Programs
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Mathematica
CoefficientList[Series[-(z + 1)^10/(z - 1)^11, {z, 0, 200}], z] (* Vladimir Joseph Stephan Orlovsky, Jun 19 2011 *)
Formula
G.f.: (1+x)^10/(1-x)^11.
a(n) = (4*n^10+20*n^9+330*n^8+1200*n^7+7392*n^6+18060*n^5+50270*n^4 +71800*n^3+83754*n^2+50670*n+14175)/14175 - Johannes W. Meijer, Jul 14 2013
Comments