OFFSET
0,2
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
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).
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
KEYWORD
nonn,nice,easy
AUTHOR
STATUS
approved