cp's OEIS Frontend

A254602 Numbers of n-length words on alphabet {0..7} with no subwords ii, where i is from {0..2}.

%I A254602 #33 Sep 08 2022 08:46:11
%S A254602 1,8,61,467,3574,27353,209341,1602152,12261769,93843143,718210846,
%T A254602 5496691637,42067895689,321958728008,2464050574501,18858147661547,
%U A254602 144327286503334,1104581743831073,8453708639334181,64698869194494632,495160627558133329,3789618738879406463
%N A254602 Numbers of n-length words on alphabet {0..7} with no subwords ii, where i is from {0..2}.
%H A254602 Colin Barker, <a href="/A254602/b254602.txt">Table of n, a(n) for n = 0..1000</a>
%H A254602 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (7,5).
%F A254602 G.f.: (1 + x)/(1 - 7*x - 5*x^2).
%F A254602 a(n) = 7*a(n-1) + 5*a(n-2) with n>1, a(0) = 1, a(1) = 8.
%F A254602 a(n) = (2^(-1-n) * ((7-sqrt(69))^n * (-9+sqrt(69)) + (7+sqrt(69))^n * (9+sqrt(69)))) / sqrt(69). - _Colin Barker_, Sep 08 2016
%p A254602 A254602:=n->(2^(-1-n) * ((7-sqrt(69))^n * (-9+sqrt(69)) + (7+sqrt(69))^n * (9+sqrt(69)))) / sqrt(69): seq(simplify(A254602(n)), n=0..30); # _Wesley Ivan Hurt_, Sep 08 2016
%t A254602 RecurrenceTable[{a[0] == 1, a[1] == 8, a[n] == 7 a[n - 1] + 5 a[n - 2]}, a[n], {n, 0, 25}]
%t A254602 LinearRecurrence[{7,5},{1,8},30] (* _Harvey P. Dale_, Jun 23 2017 *)
%o A254602 (Magma) [n le 1 select 8^n else 7*Self(n)+5*Self(n-1): n in [0..25]];
%o A254602 (PARI) Vec((1+x)/(1-7*x-5*x^2) + O(x^30)) \\ _Colin Barker_, Sep 08 2016
%Y A254602 Cf. A015562, A055099, A126473, A126501, A126528.
%K A254602 nonn,easy
%O A254602 0,2
%A A254602 _Milan Janjic_, Feb 02 2015