A008385 Coordination sequence for A_5 lattice.
1, 30, 240, 1010, 2970, 7002, 14240, 26070, 44130, 70310, 106752, 155850, 220250, 302850, 406800, 535502, 692610, 882030, 1107920, 1374690, 1687002, 2049770, 2468160, 2947590, 3493730, 4112502, 4810080, 5592890, 6467610, 7441170, 8520752
Offset: 0
Links
- T. D. Noe, 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, 1997; 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.
- J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).
- M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908.
- M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908. [Annotated scanned copy]
- Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
Programs
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Magma
[n eq 0 select 1 else (21*n^4 +35*n^2 +4)/2: n in [0..50]]; // G. C. Greubel, May 26 2023
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Maple
1, seq((21*n^4 +35*n^2 +4)/2, n=1..50);
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Mathematica
Table[n^2*(21*n^2 +35)/2 +2 -Boole[n==0], {n,0,50}] (* G. C. Greubel, May 26 2023 *) -
Maxima
A008385[n]:=21/2*n^4+35/2*n^2+2$ makelist(A008385[n],n,0,30); /* Martin Ettl, Oct 26 2012 */
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SageMath
[n^2*(21*n^2 +35)/2 +2 -int(n==0) for n in range(51)] # G. C. Greubel, May 26 2023
Formula
a(n) = (21*n^4 + 35*n^2 + 4)/2, a(0) = 1.
G.f.: (1+x)*(1+24*x+76*x^2+24*x^3+x^4)/(1-x)^5. - Colin Barker, Apr 13 2012
E.g.f.: (1/2)*(-2 + (4 + 56*x + 182*x^2 + 126*x^3 + 21*x^4)*exp(x)). - G. C. Greubel, May 26 2023