login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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

REFERENCES

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.

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.

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 15 01:25 EST 2019. Contains 329143 sequences. (Running on oeis4.)