A255633 - OEIS

%I #23 Jan 14 2024 00:14:07

%S 1,5,26,136,710,3706,19346,100990,527186,2752006,14365970,74992966,

%T 391476866,2043580150,10667858546,55688153926,290702250530,

%U 1517518403926,7921720943186,41352818219110,215869201519106,1126876333254646,5882498575587890,30707708087054086

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

%H Andrew Howroyd, <a href="/A255633/b255633.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,0,6).

%F a(n+3) = 5*a(n+2) + 6*a(n) with n > 0, a(0) = 1, a(1) = 5, a(2) = 26.

%F G.f.: (1 + x^2)/(1 - 5*x - 6*x^3). - _Andrew Howroyd_, May 01 2020

%t 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 LinearRecurrence[{5,0,6},{1,5,26},30] (* _Harvey P. Dale_, Aug 11 2023 *)

%o (PARI) Vec((1 + x^2)/(1 - 5*x - 6*x^3) + O(x^30)) \\ _Andrew Howroyd_, May 01 2020

%Y Cf. A254598, A254602, A255115, A255117, A254601, A254663.

%K nonn,easy

%O 0,2

%A _Milan Janjic_, Feb 28 2015

%E Terms a(20) and beyond from _Andrew Howroyd_, May 01 2020