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A255633 Number of n-length words on {0,1,2,3,4,5} avoiding runs of zeros of length 1 (mod 3).

%I A255633 #23 Jan 14 2024 00:14:07
%S A255633 1,5,26,136,710,3706,19346,100990,527186,2752006,14365970,74992966,
%T A255633 391476866,2043580150,10667858546,55688153926,290702250530,
%U A255633 1517518403926,7921720943186,41352818219110,215869201519106,1126876333254646,5882498575587890,30707708087054086
%N A255633 Number of n-length words on {0,1,2,3,4,5} avoiding runs of zeros of length 1 (mod 3).
%H A255633 Andrew Howroyd, <a href="/A255633/b255633.txt">Table of n, a(n) for n = 0..1000</a>
%H A255633 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,0,6).
%F A255633 a(n+3) = 5*a(n+2) + 6*a(n) with n > 0, a(0) = 1, a(1) = 5, a(2) = 26.
%F A255633 G.f.: (1 + x^2)/(1 - 5*x - 6*x^3). - _Andrew Howroyd_, May 01 2020
%t A255633 RecurrenceTable[{a[0] == 1, a[1] == 5,  a[2] == 26,  a[n] == 5* a[n - 1] +  6*a[n - 3]}, a[n], {n, 0, 20}]
%t A255633 LinearRecurrence[{5,0,6},{1,5,26},30] (* _Harvey P. Dale_, Aug 11 2023 *)
%o A255633 (PARI) Vec((1 + x^2)/(1 - 5*x - 6*x^3) + O(x^30)) \\ _Andrew Howroyd_, May 01 2020
%Y A255633 Cf. A254598, A254602, A255115, A255117, A254601, A254663.
%K A255633 nonn,easy
%O A255633 0,2
%A A255633 _Milan Janjic_, Feb 28 2015
%E A255633 Terms a(20) and beyond from _Andrew Howroyd_, May 01 2020