login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A019561 Coordination sequence for C_5 lattice. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
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
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).
Sequence in context: A111341 A222693 A228743 * A164757 A189415 A128954
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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 23 03:01 EDT 2024. Contains 373629 sequences. (Running on oeis4.)