A254659 - OEIS

%I #23 Sep 08 2022 08:46:11

%S 1,9,77,661,5673,48689,417877,3586461,30781073,264180889,2267352477,

%T 19459724261,167014556473,1433415073089,12302393367077,

%U 105586222302061,906201745251873,7777545073525289,66751369314461677,572898679883319861,4916946285638867273

%N Numbers of words on alphabet {0,1,...,8} with no subwords ii, where i is from {0,1,2,3}.

%C a(n) is the number of nonary sequences of length n such that no two consecutive terms have distance 7. - _David Nacin_, May 31 2017

%H Colin Barker, <a href="/A254659/b254659.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,5).

%F G.f.: (1 + x)/(1 - 8*x - 5*x^2).

%F a(n) = 8*a(n-1) + 5*a(n-2) with n>1, a(0) = 1, a(1) = 9.

%F a(n) = ((4-r)^n*(-5+r) + (4+r)^n*(5+r)) / (2*r), where r=sqrt(21). - _Colin Barker_, Jan 22 2017

%t RecurrenceTable[{a[0] == 1, a[1] == 9, a[n] == 8 a[n - 1] + 5 a[n - 2]}, a[n], {n, 0, 20}]

%o (Magma) [n le 1 select 9^n else 8*Self(n)+5*Self(n-1): n in [0..20]];

%o (PARI) Vec((1 + x)/(1 - 8*x -5*x^2) + O(x^30)) \\ _Colin Barker_, Jan 22 2017

%Y Cf. A015575, A055099, A126473, A126501,  A126528, A254598, A254602.

%K nonn,easy

%O 0,2

%A _Milan Janjic_, Feb 04 2015