cp's OEIS Frontend

A254662 Numbers of words on alphabet {0,1,...,7} with no subwords ii, where i is from {0,1,...,4}.

%I A254662 #16 Sep 08 2022 08:46:11
%S A254662 1,8,59,437,3236,23963,177449,1314032,9730571,72056093,533584364,
%T A254662 3951258827,29259564881,216670730648,1604473809179,11881328856197,
%U A254662 87982723420916,651523050515003,4824609523867769,35726835818619392,264561679301939051,1959112262569431533
%N A254662 Numbers of words on alphabet {0,1,...,7} with no subwords ii, where i is from {0,1,...,4}.
%H A254662 Colin Barker, <a href="/A254662/b254662.txt">Table of n, a(n) for n = 0..1000</a>
%H A254662 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (7,3).
%F A254662 G.f.: (1 + x)/(1 - 7*x -3*x^2).
%F A254662 a(n) = 7*a(n-1) + 3*a(n-2) with n>1, a(0) = 1, a(1) = 8.
%F A254662 a(n) = (2^(-1-n) * ((7-sqrt(61))^n * (-9+sqrt(61)) + (7+sqrt(61))^n * (9+sqrt(61)))) / sqrt(61). - _Colin Barker_, Sep 08 2016
%t A254662 RecurrenceTable[{a[0] == 1, a[1] == 8, a[n] == 7 a[n - 1] + 3 a[n - 2]}, a[n], {n, 0, 20}]
%o A254662 (Magma) [n le 1 select 8^n else 7*Self(n)+3*Self(n-1): n in [0..20]];
%o A254662 (PARI) Vec((1+x)/(1-7*x-3*x^2) + O(x^30)) \\ _Colin Barker_, Sep 08 2016
%Y A254662 Cf. A015559, A055099, A126473, A126501, A126528, A254598, A254602.
%K A254662 nonn,easy
%O A254662 0,2
%A A254662 _Milan Janjic_, Feb 04 2015