A022146 Coordination sequence for root lattice B_4.
1, 32, 224, 768, 1856, 3680, 6432, 10304, 15488, 22176, 30560, 40832, 53184, 67808, 84896, 104640, 127232, 152864, 181728, 214016, 249920, 289632, 333344, 381248, 433536, 490400, 552032, 618624, 690368, 767456, 850080, 938432, 1032704, 1133088, 1239776, 1352960
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- M. Baake and U. Grimm, Coordination sequences for root lattices and related graphs, arXiv:cond-mat/9706122, Zeit. f. Kristallographie, 212 (1997), 253-256.
- R. Bacher, P. de la Harpe and B. Venkov, Séries de croissance et séries d'Ehrhart associées aux réseaux de racines, C. R. Acad. Sci. Paris, 325 (Series 1) (1997), 1137-1142.
- Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
Programs
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Magma
[1] cat[32*n^3 - 16*n^2 + 16*n: n in [1..40]]; // Vincenzo Librandi, Apr 20 2012
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Mathematica
CoefficientList[Series[(1+28*x+102*x^2+60*x^3+x^4)/(1-x)^4,{x,0,40}],x] (* Vincenzo Librandi, Apr 20 2012 *)
Formula
a(0) = 1, a(n) = 32*n^3 - 16*n^2 + 16*n. - Ralf Stephan, Sep 03 2003
G.f.: (1+28*x+102*x^2+60*x^3+x^4)/(1-x)^4 = 1+32*x*(x+1)*(2*x+1)/(1-x)^4. - Colin Barker, Apr 13 2012