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A008383 Coordination sequence for A_4 lattice. 4
1, 20, 110, 340, 780, 1500, 2570, 4060, 6040, 8580, 11750, 15620, 20260, 25740, 32130, 39500, 47920, 57460, 68190, 80180, 93500, 108220, 124410, 142140, 161480, 182500, 205270, 229860, 256340, 284780, 315250, 347820, 382560, 419540, 458830, 500500, 544620 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
REFERENCES
M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908.
LINKS
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]
FORMULA
a(n) = 5*n*(7*n^2 + 5)/3, a(0) = 1.
G.f.: (1+16*x+36*x^2+16*x^3+x^4)/(1-x)^4 = 1+10*x*(2+3*x+2*x^2)/(x-1)^4. - Colin Barker, Apr 13 2012
E.g.f.: (1/3)*(3 + 5*x*(12 + 21*x + 7*x^2)*exp(x)). - G. C. Greubel, May 25 2023
MAPLE
a:= n-> `if`(n=0, 1, 35/3*n^3+25/3*n): seq (a(n), n=0..50);
MATHEMATICA
CoefficientList[Series[(1+16x+36x^2+16x^3+x^4)/(1-x)^4, {x, 0, 40}], x] (* Harvey P. Dale, Dec 01 2013 *)
Join[{1}, LinearRecurrence[{4, -6, 4, -1}, {20, 110, 340, 780}, 40]] (* Jean-François Alcover, Jan 07 2019 *)
PROG
(Magma) [n eq 0 select 1 else 5*n*(7*n^2+5)/3: n in [0..45]]; // G. C. Greubel, May 25 2023
(SageMath) [5*n*(7*n^2+5)/3+int(n==0) for n in range(46)] # G. C. Greubel, May 25 2023
CROSSREFS
Sequence in context: A189437 A285698 A109854 * A024192 A309781 A228243
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified February 22 22:43 EST 2024. Contains 370265 sequences. (Running on oeis4.)