A022145 Coordination sequence for root lattice B_3.

1, 18, 74, 170, 306, 482, 698, 954, 1250, 1586, 1962, 2378, 2834, 3330, 3866, 4442, 5058, 5714, 6410, 7146, 7922, 8738, 9594, 10490, 11426, 12402, 13418, 14474, 15570, 16706, 17882, 19098, 20354, 21650

Offset

0,2

Comments

Also sequence found by reading the segment (1, 18) together with the line from 18, in the direction 18, 74,..., in the square spiral whose vertices are the generalized dodecagonal numbers A195162. - Omar E. Pol, Nov 02 2012

Links

Vincenzo Librandi, 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.

Index entries for linear recurrences with constant coefficients, signature (3, -3, 1).

Formula

a(n) = 20*n^2-4*n+2, for n>0.

a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>3. G.f.: (1+15*x+23*x^2+x^3)/(1-x)^3. [Colin Barker, Apr 13 2012]

Mathematica

CoefficientList[Series[(1+15*x+23*x^2+x^3)/(1-x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Apr 20 2012 *)
Join[{1}, LinearRecurrence[{3, -3, 1}, {18, 74, 170}, 40]] (* Harvey P. Dale, Dec 03 2012 *)

Prog

(Magma) [1] cat [20*n^2-4*n+2: n in [1..40]]; // Vincenzo Librandi, Apr 20 2012

Crossrefs

Sequence in context: A211619 A305018 A041628 * A284659 A143666 A139757

Adjacent sequences: A022142 A022143 A022144 * A022146 A022147 A022148

Keyword

nonn,easy

Author

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

Status

approved