%I #15 Oct 12 2022 09:34:20

%S 1,3,10,34,115,388,1309,4417,14905,50296,169720,572707,1932556,

%T 6521263,22005505,74255899,250570870,845532298,2853184279,9627852832,

%U 32488455385,109629815881,369937455865,1248325741972,4212380047936

%N Numbers of words on {0,1,2,3} having no isolated zeros.

%H G. C. Greubel, <a href="/A255813/b255813.txt">Table of n, a(n) for n = 0..1000</a>

%H 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 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3,3).

%F a(n+3) = 4*a(n+2) - 3*a(n+1)+ 3*a(n) with n>=0, a(0) = 1, a(1) = 3, a(2) = 10.

%F G.f.: (-1 + x - x^2)/(-1 + 4*x - 3*x^2 + 3*x^3). - _R. J. Mathar_, Nov 07 2015

%t RecurrenceTable[{a[0] == 1, a[1] == 3, a[2]== 10, a[n] == 4 a[n - 1] - 3 a[n - 2] + 3 a[n - 3]}, a[n], {n, 0, 25}]

%t LinearRecurrence[{4, -3, 3}, {1, 3, 10}, 100] (* _G. C. Greubel_, Jun 02 2016 *)

%Y Cf. A255116, A255118, A254658, A254660, A255633, A255630

%K nonn,easy

%O 0,2

%A _Milan Janjic_, Mar 07 2015