%I #18 Dec 19 2015 01:06:11
%S 1,4,17,73,312,1333,5697,24348,104057,444713,1900592,8122653,34714177,
%T 148359668,634051937,2709778633,11580912872,49493911173,211524537857,
%U 904002715788,3863480419017,16511544365353,70566191040352
%N Number of n-length words on {0,1,2,3,4} avoiding runs of zeros of length 1 (mod 3).
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,0,5).
%F a(n+3) = 4*a(n+2) + 5*a(n) with n > 0, a(0) = 1, a(1) = 4, a(2) = 17.
%F G.f.: ( -1-x^2 ) / ( -1+4*x+5*x^3 ). - _R. J. Mathar_, Nov 07 2015
%t RecurrenceTable[{a[0] == 1, a[1] == 4, a[2] == 17, a[n] == 4*a[n - 1] + 5*a[n - 3]}, a[n], {n, 0, 23}]
%Y Cf. A254598, A254602, A255115, A255117, A254601, A254663.
%K nonn,easy
%O 0,2
%A _Milan Janjic_, Feb 28 2015