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A120925 Number of ternary words on {0,1,2} having no isolated 0's.

%I A120925 #21 Nov 16 2024 11:54:43
%S A120925 1,2,5,13,33,83,209,527,1329,3351,8449,21303,53713,135431,341473,
%T A120925 860983,2170865,5473575,13800961,34797463,87737617,221219847,
%U A120925 557779233,1406373239,3546000945,8940814823,22543189057,56839939415,143315069777
%N A120925 Number of ternary words on {0,1,2} having no isolated 0's.
%C A120925 Column 0 of A120924.
%H A120925 Michael De Vlieger, <a href="/A120925/b120925.txt">Table of n, a(n) for n = 0..2490</a>
%H A120925 D. Birmajer, J. B. Gil, and M. D. Weiner, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL19/Gil/gil6.html">On the Enumeration of Restricted Words over a Finite Alphabet</a>, J. Int. Seq. 19 (2016) # 16.1.3, example 11.
%H A120925 Maksym Druchok, Volodymyr Krasnov, Taras Krokhmalskii, and Oleg Derzhko, <a href="https://arxiv.org/abs/2307.06186">One-dimensionally confined ammonia molecules: A theoretical study</a>, arXiv:2307.06186 [cond-mat.stat-mech], 2023. See p. 5.
%H A120925 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,2).
%F A120925 a(n) = 3a(n-1)-2a(n-2)+2a(n-3); a(0)=1, a(1)=2,a(2)=5.
%F A120925 G.f.: (1-z+z^2)/(1-3z+2z^2-2z^3).
%e A120925 a(2)=5 because we have 00,11,12,21 and 22.
%p A120925 a[0]:=1:a[1]:=2:a[2]:=5: for n from 3 to 32 do a[n]:=3*a[n-1]-2*a[n-2]+2*a[n-3] od: seq(a[n],n=0..32);
%t A120925 nn=20;a=x^2/(1-x);CoefficientList[Series[(a+1)/(1-(2x a)/(1-2x))/(1-2x),{x,0,nn}],x]  (* _Geoffrey Critzer_, Jan 13 2013 *)
%t A120925 LinearRecurrence[{3,-2,2},{1,2,5},30] (* _Harvey P. Dale_, Nov 16 2024 *)
%Y A120925 Cf. A105114, A120924.
%K A120925 nonn,easy
%O A120925 0,2
%A A120925 _Emeric Deutsch_, Jul 16 2006