A254660 - OEIS

%I #22 Sep 11 2024 15:07:01

%S 1,7,44,278,1756,11092,70064,442568,2795536,17658352,111541184,

%T 704563808,4450465216,28111918912,177572443904,1121658501248,

%U 7085095895296,44753892374272,282693546036224,1785669060965888,11279401457867776,71247746869138432

%N Numbers of words on alphabet {0,1,...,6} with no subwords ii, where i is from {0,1,...,4}.

%H Colin Barker, <a href="/A254660/b254660.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,2).

%F G.f.: (1 + x)/(1 - 6*x -2*x^2).

%F a(n) = 6*a(n-1) + 2*a(n-2) with n>1, a(0) = 1, a(1) = 7.

%F a(n) = ((3-sqrt(11))^n*(-4+sqrt(11)) + (3+sqrt(11))^n*(4+sqrt(11))) / (2*sqrt(11)). - _Colin Barker_, Jan 21 2017

%t RecurrenceTable[{a[0] == 1, a[1] == 7, a[n] == 6 a[n - 1] + 2 a[n - 2]}, a[n], {n, 0, 20}]

%t LinearRecurrence[{6,2},{1,7},30] (* _Harvey P. Dale_, Sep 11 2024 *)

%o (PARI) Vec((1 + x) / (1 - 6*x -2*x^2) + O(x^30)) \\ _Colin Barker_, Jan 21 2017

%Y Cf. A135030, A126473, A126501, A126528, A254598, A254602.

%K nonn,easy

%O 0,2

%A _Milan Janjic_, Feb 04 2015