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A008387 Coordination sequence for A_6 lattice. 3
1, 42, 462, 2562, 9492, 27174, 65226, 137886, 264936, 472626, 794598, 1272810, 1958460, 2912910, 4208610, 5930022, 8174544, 11053434, 14692734, 19234194, 24836196, 31674678, 39944058, 49858158, 61651128, 75578370, 91917462, 110969082 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

R. Bacher, P. de la Harpe and B. Venkov, Series de croissance et series d'Ehrhart associees aux reseaux de racines, C. R. Acad. Sci. Paris, 325 (Series 1) (1997), 1137-1142.

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, Zeit. f. Kristallographie, 212 (1997), 253-256.

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 linear recurrences with constant coefficients, signature (6, -15, 20, -15, 6, -1).

FORMULA

a(n) = S(n,6) = 7*n*(11*n+35*n+14)/10, with S(n,d) = sum_{k=0..d} binomial(d,k)^2*binomial(n-k+d-1,d-1).

G.f.: (x^6+36*x^5+225*x^4+400*x^3+225*x^2+36*x+1)/(x-1)^6 = 1+42*x*(1+5*x+10*x^2+5*x^3+x^4)/(1-x)^6. [Colin Barker, Sep 26 2012]

MAPLE

77/10*n^5+49/2*n^3+49/5*n;

MATHEMATICA

Join[{1}, LinearRecurrence[{6, -15, 20, -15, 6, -1}, {42, 462, 2562, 9492, 27174, 65226}, 30]] (* Jean-Fran├žois Alcover, Jan 07 2019 *)

CROSSREFS

Sequence in context: A248094 A244909 A090297 * A088626 A328175 A216109

Adjacent sequences:  A008384 A008385 A008386 * A008388 A008389 A008390

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane and J. H. Conway

STATUS

approved

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Last modified September 21 01:46 EDT 2021. Contains 347596 sequences. (Running on oeis4.)