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A022145
Coordination sequence for root lattice B_3.
4
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
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.
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
KEYWORD
nonn,easy
AUTHOR
mbaake(AT)sunelc3.tphys.physik.uni-tuebingen.de (Michael Baake)
STATUS
approved