A008255 Coordination sequence T2 for feldspar.

1, 4, 10, 22, 38, 56, 82, 112, 142, 182, 226, 268, 322, 380, 434, 502, 574, 640, 722, 808, 886, 982, 1082, 1172, 1282, 1396, 1498, 1622, 1750, 1864, 2002, 2144, 2270, 2422, 2578, 2716, 2882, 3052, 3202, 3382, 3566, 3728, 3922, 4120, 4294, 4502, 4714, 4900

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

R. W. Grosse-Kunstleve, Coordination Sequences and Encyclopedia of Integer Sequences

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

Index entries for linear recurrences with constant coefficients, signature (1,0,2,-2,0,-1,1).

Formula

a(3*m) = 20*m^2+2, a(3*m+1) = 20*m^2+14*m+4, a(3*m+2) = 20*m^2+26*m+10.

G.f.: (1+x)^3*(1+3*x^2+x^4) / ((1-x)^3*(1+x+x^2)^2). - Colin Barker, Dec 22 2015

Mathematica

Table[SeriesCoefficient[(1 + x)^3 (1 + 3 x^2 + x^4)/((1 - x)^3 (1 + x + x^2)^2), {x, 0, n}], {n, 0, 47}] (* Michael De Vlieger, Dec 22 2015 *)
Join[{1}, LinearRecurrence[{1, 0, 2, -2, 0, -1, 1}, {4, 10, 22, 38, 56, 82, 112}, 50]] (* Vincenzo Librandi, Dec 23 2015 *)

Prog

(PARI) Vec((1+x)^3*(1+3*x^2+x^4)/((1-x)^3*(1+x+x^2)^2) + O(x^100)) \\ Colin Barker, Dec 22 2015

Crossrefs

Sequence in context: A009891 A301077 A341734 * A008031 A339609 A008248

Adjacent sequences: A008252 A008253 A008254 * A008256 A008257 A008258

Keyword

nonn,easy

Author

Georg Thimm (mgeorg(AT)ntu.edu.sg) and Ralf W. Grosse-Kunstleve

Status

approved