A027368 Coordination sequence T4 for Zeolite Code CGS.

1, 4, 9, 18, 32, 48, 67, 91, 119, 151, 185, 224, 268, 313, 364, 417, 472, 533, 596, 666, 737, 811, 893, 975, 1065, 1154, 1244, 1344, 1443, 1550, 1656, 1766, 1887, 2004, 2132, 2258, 2385, 2523, 2657, 2803, 2945, 3090, 3248, 3401, 3568, 3729, 3892, 4069

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

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 (2, -2, 2, -2, 3, -5, 6, -6, 6, -5, 5, -6, 6, -6, 5, -3, 2, -2, 2, -2, 1).

Formula

G.f.: (1 + x) * (1 + x + 2*x^2 + 4*x^3 + 4*x^4 + 3*x^5 + 7*x^6 + 5*x^7 + 7*x^8 + 8*x^9 + 8*x^10 + 8*x^11 + 7*x^12 + 5*x^13 + 7*x^14 + 3*x^15 + 4*x^16 + 4*x^17 + 2*x^18 + x^19 + x^20) / ((1 - x)^3 * (1 + x^2) * (1 - x + x^2 - x^3 + x^4) * (1 - x^2 + x^4) * (1 + x + x^2 + x^3 + x^4)^2). - Colin Barker, Dec 21 2015

a(n) ~ 46*n^2/25. - Charles R Greathouse IV, Jun 02 2026

Mathematica

CoefficientList[Series[(1+x)(1+x+2x^2+4x^3+4x^4+3x^5+7x^6+5x^7+7x^8+8x^9+8x^10+8x^11+7x^12+5x^13+7x^14+3x^15+4x^16+4x^17+2x^18+x^19+x^20)/((1-x)^3(1+x^2)(1-x+x^2-x^3+x^4)(1-x^2+x^4)(1+x+x^2+x^3+x^4)^2), {x, 0, 70}], x] (* Harvey P. Dale, Mar 19 2026 *)
(* Alternative: *)
LinearRecurrence[{2, -2, 2, -2, 3, -5, 6, -6, 6, -5, 5, -6, 6, -6, 5, -3, 2, -2, 2, -2, 1}, {1, 4, 9, 18, 32, 48, 67, 91, 119, 151, 185, 224, 268, 313, 364, 417, 472, 533, 596, 666, 737, 811}, 70] (* Harvey P. Dale, Mar 19 2026 *)

Crossrefs

Sequence in context: A254874 A301146 A027366 * A008266 A301200 A008222

Adjacent sequences: A027365 A027366 A027367 * A027369 A027370 A027371

Keyword

nonn,easy,changed

Author

Ralf W. Grosse-Kunstleve

Status

approved