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A008253 Coordination sequence for diamond. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
REFERENCES
Inorganic Crystal Structure Database: Collection Code 9327.
LINKS
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.
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.
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)
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 *)
PROG
(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
CROSSREFS
Sequence in context: A008215 A008232 A008175 * A057308 A301006 A008158
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified September 30 18:30 EDT 2023. Contains 365793 sequences. (Running on oeis4.)