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A022145 Coordination sequence for root lattice B_3. 4


%S 1,18,74,170,306,482,698,954,1250,1586,1962,2378,2834,3330,3866,4442,

%T 5058,5714,6410,7146,7922,8738,9594,10490,11426,12402,13418,14474,

%U 15570,16706,17882,19098,20354,21650

%N Coordination sequence for root lattice B_3.

%C 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

%D R. Bacher, P. de la Harpe and B. Venkov, Series de croissance et series d'Ehrhart associees aux reseaux de racines, C. R. Acad. Sci. Paris, 325 (Series 1) (1997), 1137-1142.

%H Vincenzo Librandi, <a href="/A022145/b022145.txt">Table of n, a(n) for n = 0..1000</a>

%H M. Baake and U. Grimm, <a href="https://arxiv.org/abs/cond-mat/9706122">Coordination sequences for root lattices and related graphs</a>, arXiv:cond-mat/9706122, Zeit. f. Kristallographie, 212 (1997), 253-256.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3, -3, 1).

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

%F 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]

%t CoefficientList[Series[(1+15*x+23*x^2+x^3)/(1-x)^3,{x,0,40}],x] (* _Vincenzo Librandi_, Apr 20 2012 *)

%t Join[{1},LinearRecurrence[{3,-3,1},{18,74,170},40]] (* _Harvey P. Dale_, Dec 03 2012 *)

%o (MAGMA) [1] cat [20*n^2-4*n+2: n in [1..40]]; // _Vincenzo Librandi_, Apr 20 2012

%K nonn,easy

%O 0,2

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

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Last modified December 14 01:33 EST 2019. Contains 329978 sequences. (Running on oeis4.)