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A254601 Numbers of n-length words on alphabet {0,1,...,6} with no subwords ii, where i is from {0,1,2}.

%I A254601 #32 Sep 08 2022 08:46:11
%S A254601 1,7,46,304,2008,13264,87616,578752,3822976,25252864,166809088,
%T A254601 1101865984,7278432256,48078057472,317582073856,2097804673024,
%U A254601 13857156333568,91534156693504,604633565495296,3993938019745792,26382162380455936,174268726361718784
%N A254601 Numbers of n-length words on alphabet {0,1,...,6} with no subwords ii, where i is from {0,1,2}.
%H A254601 Colin Barker, <a href="/A254601/b254601.txt">Table of n, a(n) for n = 0..1000</a>
%H A254601 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,4).
%F A254601 G.f.: (1 + x)/(1 - 6*x - 4*x^2).
%F A254601 a(n) =  6*a(n-1) + 4*a(n-2) with n>1, a(0) = 1, a(1) = 7.
%F A254601 a(n) = ((3-r)^n*(-4+r) + (3+r)^n*(4+r)) / (2*r), where r=sqrt(13). - _Colin Barker_, Jan 22 2017
%F A254601 a(n) = A135032(n-1)+A135032(n). - _R. J. Mathar_, Apr 07 2022
%t A254601 RecurrenceTable[{a[0] == 1, a[1] == 7, a[n] == 6 a[n - 1] + 4 a[n - 2]}, a[n], {n, 0, 25}]
%t A254601 LinearRecurrence[{6,4},{1,7},30] (* _Harvey P. Dale_, Oct 10 2017 *)
%o A254601 (Magma) [n le 1 select 7^n else 6*Self(n)+4*Self(n-1): n in [0..25]]; // _Bruno Berselli_, Feb 03 2015
%o A254601 (PARI) Vec((1 + x)/(1 - 6*x - 4*x^2) + O(x^30)) \\ _Colin Barker_, Jan 22 2017
%Y A254601 Cf. A055099, A126473, A126501, A126528, A135032, A190976 (shifted bin. trans).
%K A254601 nonn,easy
%O A254601 0,2
%A A254601 _Milan Janjic_, Feb 02 2015