A019561 Coordination sequence for C_5 lattice.

1, 50, 450, 1970, 5890, 14002, 28610, 52530, 89090, 142130, 216002, 315570, 446210, 613810, 824770, 1086002, 1404930, 1789490, 2248130, 2789810, 3424002, 4160690, 5010370, 5984050, 7093250, 8350002

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 (5,-10,10,-5,1).

Formula

G.f.: (1+45*x+210*x^2+210*x^3+45*x^4+x^5)/(1-x)^5 = 1+2*x*(5+10*x+x^2)^2/(1-x)^5.

G.f. for sequence with interpolated zeros: cosh(10*arctanh(x)) = 1/2*( ((1 + x)/(1 - x))^5 + ((1 - x)/(1 + x))^5 ) = 1 + 50*x^2 + 450*x^4 + 1970*x^6 + .... - Peter Bala, Apr 09 2017

a(n) = A008413(2*n). - Seiichi Manyama, Jun 08 2018

Mathematica

LinearRecurrence[{5, -10, 10, -5, 1}, {1, 50, 450, 1970, 5890, 14002}, 30] (* Harvey P. Dale, Nov 21 2021 *)

Crossrefs

Cf. A103884 (row 5). For coordination sequences of other C_n lattices see A022144 (C_2), A010006 (C3), A019560 - A019564 (C_4 through C_8), A035746 - A035787 (C_9 through C_50).

Cf. A008413, A137513.

Sequence in context: A111341 A222693 A228743 * A164757 A189415 A128954

Adjacent sequences: A019558 A019559 A019560 * A019562 A019563 A019564

Keyword

nonn,easy

Author

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

Status

approved