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A254598 Numbers of n-length words on alphabet {0,1,...,8} with no subwords ii, for i from {0,1}.

%I A254598 #47 Feb 13 2020 11:48:34
%S A254598 1,9,79,695,6113,53769,472943,4159927,36590017,321839625,2830847119,
%T A254598 24899654327,219013164449,1926402895881,16944315318191,
%U A254598 149039342816695,1310924949760897,11530674997804041,101421874630758607,892089722030697143,7846670898660887393,69017995243501979145
%N A254598 Numbers of n-length words on alphabet {0,1,...,8} with no subwords ii, for i from {0,1}.
%C A254598 Is this essentially A251366? - _Bruno Berselli_, Feb 02 2015
%C A254598 Yes, it is: see proof at A251366. - _Robert Israel_, Mar 19 2018
%C A254598 a(n) is the number of nonary sequences of length n such that no two consecutive terms have distance 8. - _David Nacin_, May 31 2017
%H A254598 Colin Barker, <a href="/A254598/b254598.txt">Table of n, a(n) for n = 0..1000</a>
%H A254598 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,7).
%F A254598 a(n) = 8*a(n-1) + 7*a(n-2) with n>1, a(0) = 1, a(1) = 9.
%F A254598 G.f.: -(x+1) / (7*x^2 + 8*x - 1). - _Colin Barker_, Feb 02 2015
%F A254598 a(n) = (((4-sqrt(23))^n * (-5+sqrt(23)) + (4+sqrt(23))^n * (5+sqrt(23)))) / (2*sqrt(23)). - _Colin Barker_, Sep 08 2016
%F A254598 a(n) = A015576(n) + A015576(n+1). - _R. J. Mathar_, Feb 13 2020
%p A254598 f:= gfun:-rectoproc({a(n) = 8*a(n-1) + 7*a(n-2), a(0)=1, a(1)=9},a(n), remember):
%p A254598 map(f, [$0..30]); # _Robert Israel_, Mar 19 2018
%t A254598 RecurrenceTable[{a[0] == 1, a[1] == 9, a[n] == 8 a[n - 1] + 7 a[n - 2]}, a[n], {n, 0, 25}] (* _Bruno Berselli_, Feb 03 2015 *)
%t A254598 LinearRecurrence[{8,7},{1,9},30] (* _Harvey P. Dale_, Oct 14 2017 *)
%o A254598 (PARI) Vec(-(x+1)/(7*x^2+8*x-1) + O(x^100)) \\ _Colin Barker_, Feb 02 2015
%Y A254598 Cf. A015576, A251366.
%K A254598 nonn,easy
%O A254598 0,2
%A A254598 _Milan Janjic_, Feb 02 2015