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Coordination sequence T3 for Zeolite Code OWE.
1

%I #9 Feb 03 2021 21:55:21

%S 1,4,11,22,32,49,77,109,139,163,197,250,310,357,398,456,526,603,676,

%T 744,819,903,999,1097,1191,1283,1386,1504,1619,1732,1850,1978,2113,

%U 2244,2374,2517,2673,2825,2973,3125,3287,3460,3638,3813,3982,4158,4348

%N Coordination sequence T3 for Zeolite Code OWE.

%H R. W. Grosse-Kunstleve, <a href="/A301152/b301152.txt">Table of n, a(n) for n = 0..1000</a>

%H Sean A. Irvine, <a href="/A008000/a008000_1.pdf">Generating Functions for Coordination Sequences of Zeolites, after Grosse-Kunstleve, Brunner, and Sloane</a>

%H International Zeolite Association, <a href="http://www.iza-structure.org/databases/">Database of Zeolite Structures</a>

%H <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (1,-2,2,-2,3,-2,4,-3,4,-4,3,-4,2,-3,2,-2,2,-1,1).

%F From _Chai Wah Wu_, Feb 03 2021: (Start)

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

%F G.f.: -(x + 1)*(x^18 + 2*x^17 + 7*x^16 + 10*x^15 + 16*x^14 + 28*x^13 + 32*x^12 + 49*x^11 + 44*x^10 + 54*x^9 + 44*x^8 + 49*x^7 + 32*x^6 + 28*x^5 + 16*x^4 + 10*x^3 + 7*x^2 + 2*x + 1)/((x - 1)^3*(x^2 + 1)*(x^2 - x + 1)*(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)

%K nonn

%O 0,2

%A _Sean A. Irvine_, Mar 18 2018