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%I #23 Oct 12 2022 09:34:17
%S 1,4,17,73,313,1341,5745,24613,105449,451773,1935521,8292309,35526553,
%T 152205613,652091089,2793739205,11969154121,51279178141,219694231041,
%U 941231059125,4032495084025,17276328107789,74016584439345,317107590101669
%N Numbers of words on {0,1,2,3,4,} having no isolated zeros.
%H G. C. Greubel, <a href="/A255814/b255814.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 (5,-4,4).
%F a(n+3) = 5*a(n+2) - 4*a(n+1)+ 4*a(n) with n>=0, a(0) = 1, a(1) = 4, a(2) = 17.
%F G.f.: (-1 + x - x^2)/(-1 + 5*x - 4*x^2 + 4*x^3). - _R. J. Mathar_, Nov 07 2015
%t RecurrenceTable[{a[0] == 1, a[1] == 4, a[2]== 17, a[n] == 5 a[n - 1] - 4 a[n - 2] + 4 a[n - 3]}, a[n], {n, 0, 23}]
%t LinearRecurrence[{5, -4, 4}, {1, 4, 17}, 100] (* _G. C. Greubel_, Jun 02 2016 *)
%t CoefficientList[Series[(-1 + x - x^2) / (-1 + 5 x -4 x^2 + 4 x^3), {x, 0, 33}], x] (* _Vincenzo Librandi_, Feb 26 2018 *)
%o (Magma) I:=[1,4,17]; [n le 3 select I[n] else 5*Self(n-1)-4*Self(n-2)+4*Self(n-3): n in [1..30]]; // _Vincenzo Librandi_, Feb 26 2018
%Y Cf. A255116, A255118, A254658, A254660, A255633, A255630.
%K nonn,easy
%O 0,2
%A _Milan Janjic_, Mar 07 2015
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