cp's OEIS Frontend

A254599 Numbers of words on alphabet {0,1,...,9} with no subwords ii, for i from {0,1}.

%I A254599 #23 Sep 08 2022 08:46:11
%S A254599 1,10,98,962,9442,92674,909602,8927810,87627106,860066434,8441614754,
%T A254599 82855064258,813228496354,7981896981250,78342900802082,
%U A254599 768941283068738,7547214754035298,74076463050867586,727065885490090658,7136204673817756610,70042369148280534754
%N A254599 Numbers of words on alphabet {0,1,...,9} with no subwords ii, for i from {0,1}.
%C A254599 a(n) is the number of sequences over {0,1,...,9} of length n such that no two consecutive terms have distance 9. - _David Nacin_, May 31 2017
%H A254599 Colin Barker, <a href="/A254599/b254599.txt">Table of n, a(n) for n = 0..1000</a>
%H A254599 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (9,8).
%F A254599 a(n) = 9*a(n-1) + 8*a(n-2) with n>1, a(0) = 1, a(1) = 10.
%F A254599 G.f.: (1 + x)/(1 - 9*x - 8*x^2). - _Bruno Berselli_, Feb 02 2015
%F A254599 a(n) = (2^(-1-n)*((9-r)^n*(-11+r) + (9+r)^n*(11+r))) / r, where r=sqrt(113). - _Colin Barker_, Jan 22 2017
%t A254599 RecurrenceTable[{a[0] == 1, a[1] == 10, a[n] == 9 a[n - 1] + 8 a[n - 2]}, a[n], {n, 0, 20}] (* _Bruno Berselli_, Feb 02 2015 *)
%o A254599 (Magma) [n le 1 select 10^n else 9*Self(n)+8*Self(n-1): n in [0..20]]; // _Bruno Berselli_, Feb 02 2015
%o A254599 (PARI) Vec((1 + x)/(1 - 9*x - 8*x^2) + O(x^30)) \\ _Colin Barker_, Jan 22 2017
%Y A254599 Cf. A015584, A055099, A126473, A126501, A126528.
%K A254599 nonn,easy
%O A254599 0,2
%A A254599 _Milan Janjic_, Feb 02 2015