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
KEYWORD
nonn,easy
AUTHOR
Georg Thimm (mgeorg(AT)ntu.edu.sg) and Ralf W. Grosse-Kunstleve
STATUS
approved