cp's OEIS Frontend

A254600 Numbers of words on alphabet {0,1,...,10} with no subwords ii, for i from {0,1}.

%I A254600 #37 Sep 08 2022 08:46:11
%S A254600 1,11,119,1289,13961,151211,1637759,17738489,192124721,2080893611,
%T A254600 22538058599,244108628489,2643928812281,28636265779211,
%U A254600 310158017102639,3359306563039289,36384487784316641,394078636910520011,4268246759164049879,46229175323835178889
%N A254600 Numbers of words on alphabet {0,1,...,10} with no subwords ii, for i from {0,1}.
%C A254600 a(n) equals the number of sequences over the alphabet {0,1,...,9,10} such that no two consecutive terms have distance 10. - _David Nacin_, Jun 02 2017
%H A254600 Colin Barker, <a href="/A254600/b254600.txt">Table of n, a(n) for n = 0..950</a>
%H A254600 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,9).
%F A254600 G.f.: (1+x)/(1-10*x-9*x^2).
%F A254600 a(n) = 10*a(n-1) + 9*a(n-2) with n>1, a(0) = 1, a(1) = 11.
%F A254600 a(n) = ((5-sqrt(34))^n*(-6+sqrt(34)) + (5+sqrt(34))^n*(6+sqrt(34))) / (2*sqrt(34)). - _Colin Barker_, Jan 21 2017
%F A254600 a(n) = (-3*i)^(n-1) * (ChebyshevU(n-1, 5*i/3) - 3*i*ChebyshevU(n, 5*i/3)). - _G. C. Greubel_, Feb 13 2021
%t A254600 RecurrenceTable[{a[0]==1, a[1]==11, a[n]== 10a[n-1] +9a[n-2]}, a[n], {n, 0, 25}]
%t A254600 Table[(-3 I)^(n-1)*(ChebyshevU[n-1, 5*I/3] - 3*I*ChebyshevU[n, 5*I/3]), {n,0,25}] (* _G. C. Greubel_, Feb 13 2021 *)
%o A254600 (Magma) [n le 1 select 11^n else 10*Self(n)+9*Self(n-1): n in [0..20]]; // _Bruno Berselli_, Feb 03 2015
%o A254600 (PARI) Vec((x+1) / (1-10*x-9*x^2) + O(x^30)) \\ _Colin Barker_, Jan 21 2017
%o A254600 (Sage) [(-3*i)^(n-1)*( chebyshev_U(n-1, 5*i/3) -3*i*chebyshev_U(n, 5*i/3) ) for n in (0..30)] # _G. C. Greubel_, Feb 13 2021
%Y A254600 Cf. A015591, A055099, A126473, A126501, A126528.
%K A254600 nonn,easy
%O A254600 0,2
%A A254600 _Milan Janjic_, Feb 02 2015