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
KEYWORD
nonn
AUTHOR
Sean A. Irvine, Mar 18 2018
STATUS
approved