A019563 Coordination sequence for C_7 lattice.

1, 98, 1666, 12642, 59906, 209762, 596610, 1459810, 3188738, 6376034, 11879042, 20889442, 35011074, 56345954, 87588482, 132127842, 194158594, 278799458, 392220290, 541777250, 736156162, 985524066

Offset: 0

Author

Michael Baake (mbaake(AT)sunelc3.tphys.physik.uni-tuebingen.de)

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• 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.
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

Cf. A008415.

Programs

Magma

m:=30; R:=PowerSeriesRing(Integers(), m); Coefficients(R!( (x+1)*(1+90*x+911*x^2+2092*x^3+911*x^4 + 90*x^5+x^6)/(1-x)^7 )); // G. C. Greubel, Dec 08 2018

Maple

seq(coeff(series((x+1)*(1+90*x+911*x^2+2092*x^3+911*x^4+90*x^5+x^6)/(1-x)^7,x,n+1), x, n), n = 0 .. 30); # Muniru A Asiru, Dec 08 2018

Mathematica

Join[{1}, LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {98, 1666, 12642, 59906, 209762, 596610, 1459810}, 21]] (* Jean-François Alcover, Dec 08 2018 *)

PARI

my(x='x+O('x^30)); Vec((x+1)*(1+90*x+911*x^2+2092*x^3+911*x^4 + 90*x^5+x^6)/(1-x)^7) \\ G. C. Greubel, Dec 08 2018

Sage

s=((x+1)*(1+90*x+911*x^2+2092*x^3+911*x^4 + 90*x^5+x^6)/(1-x)^7 ).series(x, 30); s.coefficients(x, sparse=False) # G. C. Greubel, Dec 08 2018

Formula

G.f.: (x + 1)*(1 + 90*x + 911*x^2 + 2092*x^3 + 911*x^4 + 90*x^5 + x^6)/(1 - x)^7.

a(n) = A008415(2*n). - Seiichi Manyama, Jun 08 2018