A301150 Coordination sequence T1 for Zeolite Code OWE.

1, 4, 9, 18, 35, 57, 76, 96, 128, 172, 216, 252, 290, 343, 408, 471, 528, 591, 665, 745, 828, 912, 996, 1084, 1184, 1292, 1396, 1498, 1609, 1732, 1858, 1980, 2104, 2239, 2383, 2525, 2664, 2812, 2972, 3135, 3297, 3460, 3626, 3799, 3984, 4175, 4359

Offset

0,2

Links

R. W. Grosse-Kunstleve, Table of n, a(n) for n = 0..1000

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 (3,-6,9,-11,12,-12,13,-15,18,-20,20,-18,15,-13,12,-12,11,-9,6,-3,1).

Formula

From Chai Wah Wu, Apr 24 2024: (Start)

a(n) = 3*a(n-1) - 6*a(n-2) + 9*a(n-3) - 11*a(n-4) + 12*a(n-5) - 12*a(n-6) + 13*a(n-7) - 15*a(n-8) + 18*a(n-9) - 20*a(n-10) + 20*a(n-11) - 18*a(n-12) + 15*a(n-13) - 13*a(n-14) + 12*a(n-15) - 12*a(n-16) + 11*a(n-17) - 9*a(n-18) + 6*a(n-19) - 3*a(n-20) + a(n-21) for n > 21.

G.f.: -(x + 1)*(x^20 + 3*x^18 + 3*x^17 + 7*x^16 + 4*x^15 + 12*x^14 + 8*x^13 + 15*x^12 + 13*x^11 + 12*x^10 + 13*x^9 + 15*x^8 + 8*x^7 + 12*x^6 + 4*x^5 + 7*x^4 + 3*x^3 + 3*x^2 + 1)/((x - 1)^3*(x^2 + 1)*(x^2 - x + 1)*(x^4 - x^3 + x^2 - x + 1)*(x^4 + x^3 + x^2 + x + 1)*(x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)). (End)

Crossrefs

Sequence in context: A301104 A038089 A333394 * A301078 A320851 A027053

Adjacent sequences: A301147 A301148 A301149 * A301151 A301152 A301153

Keyword

nonn

Author

Sean A. Irvine, Mar 18 2018

Status

approved