A008121 Coordination sequence T1 for Zeolite Code JBW.

1, 4, 10, 21, 39, 61, 81, 107, 148, 192, 228, 266, 324, 393, 449, 503, 575, 659, 738, 814, 906, 1002, 1090, 1191, 1311, 1427, 1521, 1629, 1780, 1926, 2036, 2148, 2308, 2487, 2625, 2753, 2919, 3105, 3274, 3432, 3618, 3808, 3978, 4169, 4391, 4601, 4769, 4959

Offset

0,2

Links

R. W. Grosse-Kunstleve, 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

International Zeolite Association, Database of Zeolite Structures

Index entries for linear recurrences with constant coefficients, signature (0,1,-2,2,-1,3,-2,4,-4,2,-3,1,-2,2,-1,1).

Formula

G.f.: (1 + x) * (1 - x + x^2) * (1 + 3*x + 8*x^2 + 16*x^3 + 28*x^4 + 37*x^5 + 40*x^6 + 37*x^7 + 28*x^8 + 16*x^9 + 8*x^10 + 3*x^11 + x^12) / ((1 - x)^3 * (1 + x^2)^2 * (1 + x + x^2 + x^3 + x^4)^2). - Colin Barker, Dec 18 2015

Mathematica

CoefficientList[Series[(1 + x) * (1 - x + x^2) * (1 + 3*x + 8*x^2 + 16*x^3 + 28*x^4 + 37*x^5 + 40*x^6 + 37*x^7 + 28*x^8 + 16*x^9 + 8*x^10 + 3*x^11 + x^12) / ((1 - x)^3 * (1 + x^2)^2 * (1 + x + x^2 + x^3 + x^4)^2), {x, 0, 47}], x] (* Stefano Spezia, Dec 22 2022 *)

Crossrefs

Cf. A005897, A008000.

Sequence in context: A009898 A301213 A358042 * A253687 A253688 A049480

Adjacent sequences: A008118 A008119 A008120 * A008122 A008123 A008124

Keyword

nonn,easy

Author

Ralf W. Grosse-Kunstleve

Status

approved