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A008361 Coordination sequence for D_8 lattice. 2
1, 112, 2592, 25424, 149568, 629808, 2100832, 5910288, 14610560, 32641008, 67232416, 129565392, 236214464, 410909616, 686647008, 1108180624, 1734926592, 2644311920, 3935599392, 5734220368 (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 (8,-28,56,-70,56,-28,8,-1).

FORMULA

a(n) = 16/315*n*(219 + 1036*n^2 + 826*n^4 + 124*n^6). - Harvey P. Dale, Feb 21 2012

a(0)=1, a(1)=112, a(2)=2592, a(3)=25424, a(4)=149568, a(5)=629808, a(6)=2100832, a(7)=5910288, a(8)=14610560, a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8). - Harvey P. Dale, Feb 21 2012

G.f.: (x^8 + 104*x^7 + 1724*x^6 + 7768*x^5 + 12550*x^4 + 7768*x^3 + 1724*x^2 + 104*x + 1)/(x - 1)^8. - Colin Barker, Sep 26 2012

MAPLE

1984/315*n^7+1888/45*n^5+2368/45*n^3+1168/105*n;

MATHEMATICA

Join[{1}, Table[16/315*n*(219+1036*n^2+826*n^4+124*n^6), {n, 30}]] (* or *) Join[{1}, LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {112, 2592, 25424, 149568, 629808, 2100832, 5910288, 14610560}, 30]] (* Harvey P. Dale, Feb 21 2012 *)

PROG

(PARI) a(n) = 16/315*n*(219 + 1036*n^2 + 826*n^4 + 124*n^6) \\ Charles R Greathouse IV, Feb 10 2017

CROSSREFS

A row of array A103903.

Sequence in context: A188153 A163194 A267327 * A271671 A172129 A304552

Adjacent sequences:  A008358 A008359 A008360 * A008362 A008363 A008364

KEYWORD

nonn,nice,easy

AUTHOR

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

STATUS

approved

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Last modified August 17 17:08 EDT 2019. Contains 326059 sequences. (Running on oeis4.)