|
| |
|
|
A022144
|
|
Coordination sequence for root lattice B_2.
|
|
10
| |
|
|
1, 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136, 144, 152, 160, 168, 176, 184, 192, 200, 208, 216, 224, 232, 240, 248, 256, 264, 272, 280, 288, 296, 304, 312, 320, 328, 336, 344, 352, 360
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| Number of points of L_infinity norm n in the simple square lattice Z^2. - N. J. A. Sloane (njas(AT)research.att.com), Apr 15 2008
Apart from initial term(s), dimension of the space of weight 2n cusp forms for Gamma_0( 24 ).
Number of 4 X n binary matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (01;0), (11;0) and (01;1). An occurrence of a ranpp (xy;z) in a matrix A=(a(i,j)) is a triple (a(i1,j1), a(i1,j2), a(i2,j1)) where i1<i2, j1<j2 and these elements are in same relative order as those in the triple (x,y,z). - Sergey Kitaev (kitaev(AT)ms.uky.edu), Nov 11 2004
These numbers correspond to the number of primes in the shells of a prime spiral. In a(2) there are 8 primes surrounding 2 in a prime spiral - Enoch Haga (Enokh(AT)comcast.net), Apr 06 2000.
|
|
|
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.
J. Serra-Sagrista, Enumeration of lattice points in l_1 norm, Information Processing Letters, 76, no. 1-2 (2000), 39-44.
|
|
|
LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..10000
S. Kitaev, On multi-avoidance of right angled numbered polyomino patterns, Integers: Electronic Journal of Combinatorial Number Theory 4 (2004), A21, 20pp.
S. Kitaev, On multi-avoidance of right angled numbered polyomino patterns, University of Kentucky Research Reports (2004).
William A. Stein, Dimensions of the spaces S_k(Gamma_0(N))
William A. Stein, The modular forms database
|
|
|
FORMULA
| ((1+x)/(1-x))^2 if norm is even; otherwise 0.
G.f. for coordination sequence of B_n lattice: Sum(binomial(2*n+1, 2*i)*z^i, i=0..n)-2*n*z*(1+z)^(n-1))/(1-z)^n. [Bacher et al.]
a(n) = (2n+1)^2 - (2n-1)^2. Binomial transform of [1, 7, 1, -1, 1, -1, 1,...] - Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 27 2007
a(n) = 0^n+8*n; [Vincenzo Librandi, aug 21 2011]
|
|
|
MATHEMATICA
| a=1; lst={a}; Do[b=n^2-a; AppendTo[lst, b]; a+=b, {n, 3, 6!, 2}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), May 18 2009]
|
|
|
PROG
| (MAGMA) [0^n+8*n: n in [0..50] ]; // Vincenzo Librandi, Aug 21 2011
|
|
|
CROSSREFS
| Essentially the same as A008590.
Sequence in context: A044848 A044893 A185359 * A181390 A008590 A186544
Adjacent sequences: A022141 A022142 A022143 * A022145 A022146 A022147
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| mbaake(AT)sunelc3.tphys.physik.uni-tuebingen.de (Michael Baake)
|
| |
|
|
