A254657 - OEIS

%I #16 Sep 08 2022 08:46:11

%S 1,9,78,678,5892,51204,444984,3867096,33606672,292055952,2538087648,

%T 22057036896,191684821056,1665820789824,14476675244928,

%U 125808326698368,1093326665056512,9501463280642304,82571666235477504,717582109567673856,6236086873954255872

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

%H Colin Barker, <a href="/A254657/b254657.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 (8,6).

%F G.f.: (1 + x)/(1 - 8*x - 6*x^2).

%F a(n) = 8*a(n-1) + 6*a(n-2) with n>1, a(0) = 1, a(1) = 9.

%F a(n) = (((4-sqrt(22))^n*(-5+sqrt(22)) + (4+sqrt(22))^n*(5+sqrt(22))))/(2*sqrt(22)). - _Colin Barker_, Nov 16 2016

%t RecurrenceTable[{a[0] == 1, a[1] == 9, a[n] == 8 a[n - 1] + 6 a[n - 2]}, a[n], {n, 0, 20}]

%o (Magma) [n le 1 select 9^n else 8*Self(n)+6*Self(n-1): n in [0..20]];

%o (PARI) Vec((1+x)/(1-8*x-6*x^2) + O(x^30)) \\ _Colin Barker_, Nov 16 2016

%Y Cf. A055099, A126473, A126501,  A126528, A190560, A254598, A254602.

%K nonn,easy

%O 0,2

%A _Milan Janjic_, Feb 04 2015