A008262 Coordination sequence T1 for Scapolite.

1, 4, 11, 20, 40, 68, 93, 120, 157, 206, 254, 299, 355, 430, 495, 549, 633, 735, 813, 886, 995, 1111, 1207, 1306, 1434, 1573, 1687, 1798, 1949, 2114, 2243, 2377, 2552, 2727, 2879, 3036, 3224, 3426, 3604, 3766, 3977, 4212, 4397, 4578, 4819, 5067, 5270, 5478

Offset

0,2

References

Inorganic Crystal Structure Database: Collection Code 9502.

Links

Sean A. Irvine, 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

Formula

G.f.: -(2*x^27 +3*x^25 +3*x^24 +10*x^23 +20*x^22 +43*x^21 +67*x^20 +114*x^19 +151*x^18 +211*x^17 +257*x^16 +303*x^15 +338*x^14 +354*x^13 +358*x^12 +338*x^11 +305*x^10 +261*x^9 +211*x^8 +155*x^7 +116*x^6 +67*x^5 +45*x^4 +18*x^3 +10*x^2 +3*x +1)*(1 +x)*(-1 +x^2)^2 / (-1 +x^4)^2 / (-1 +x^6) / (-1 +x^7) / (-1 +x^9).

Mathematica

Table[SeriesCoefficient[-(2 x^27 + 3 x^25 + 3 x^24 + 10 x^23 + 20 x^22 + 43 x^21 + 67 x^20 + 114 x^19 + 151 x^18 + 211 x^17 + 257 x^16 + 303 x^15 + 338 x^14 + 354 x^13 + 358 x^12 + 338 x^11 + 305 x^10 + 261 x^9 + 211*x^8 + 155 x^7 + 116 x^6 + 67 x^5 + 45 x^4 + 18 x^3 + 10 x^2 + 3 x + 1) (1 + x) (-1 + x^2)^2/(-1 + x^4)^2/(-1 + x^6)/(-1 + x^7)/(-1 + x^9), {x, 0, n}], {n, 0, 47}] (* Michael De Vlieger, Dec 23 2015 *)

Crossrefs

Sequence in context: A038413 A008174 A363604 * A075099 A240784 A345434

Adjacent sequences: A008259 A008260 A008261 * A008263 A008264 A008265

Keyword

nonn,easy

Author

Ralf W. Grosse-Kunstleve

Status

approved