A008253 Coordination sequence for diamond.
1, 4, 12, 24, 42, 64, 92, 124, 162, 204, 252, 304, 362, 424, 492, 564, 642, 724, 812, 904, 1002, 1104, 1212, 1324, 1442, 1564, 1692, 1824, 1962, 2104, 2252, 2404, 2562, 2724, 2892, 3064, 3242, 3424, 3612, 3804, 4002, 4204, 4412, 4624, 4842, 5064, 5292, 5524
Offset: 0
References
- Inorganic Crystal Structure Database: Collection Code 9327.
Links
- N. J. A. Sloane, Table of n, a(n) for n = 0..1000
- J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).
- R. W. Grosse-Kunstleve, G. O. Brunner and N. J. A. Sloane, Algebraic Description of Coordination Sequences and Exact Topological Densities for Zeolites, Acta Cryst., A52 (1996), pp. 879-889.
- Sean A. Irvine, Generating Functions for Coordination Sequences of Zeolites, after Grosse-Kunstleve, Brunner, and Sloane
- M. O'Keeffe, M. A. Peskov, S. J. Ramsden, and O. M. Yaghi, The reticular chemistry structure resource (RCSR) database of, and symbols for, crystal nets, Accounts of Chemical Research, (2008), 1782-1789. See p. 1786.
- Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).
Programs
-
Mathematica
{1}~Join~Table[2 (2 + Sum[Floor[(5 k + 3)/2], {k, n - 1}]), {n, 50}] (* Alexander Adamchuk, May 23 2006, edited by Michael De Vlieger, May 31 2022 *) -
PARI
Vec((1 + 2*x + 4*x^2 + 2*x^3 + x^4) / ((1 - x)^3*(1 + x)) + O(x^60)) \\ Colin Barker, Mar 21 2017
Formula
G.f.: (1 + 2*x + 4*x^2 + 2*x^3 + x^4) / ((1 - x)^3*(1 + x)).
a(2*m) = 10*m^2+2, a(2*m+1) = 10*m^2+10*m+4 (N. J. A. Sloane).
Apart from first term, first differences of A007904(n). - Alexander Adamchuk, May 23 2006
a(n) = 2* ( 2 + Sum_{k=1..n-1} floor((5*k+3)/2) ). - Alexander Adamchuk, May 23 2006
From Colin Barker, Mar 21 2017: (Start)
a(n) = (5*n^2 + 4)/2 for n>0 and even.
a(n) = (5*n^2 + 3)/2 for n odd.
a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n>4.
(End)