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

0,2

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).

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

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 *)

Prog

(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
(Magma) m:=30; R<x>:=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
(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

Crossrefs

Cf. A008415.

Sequence in context: A233373 A221747 A190636 * A285045 A197616 A022149

Adjacent sequences: A019560 A019561 A019562 * A019564 A019565 A019566

Keyword

nonn

Author

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

Status

approved