A287819 - OEIS

%I #12 Apr 09 2020 10:52:41

%S 1,9,71,561,4433,35031,276827,2187585,17287073,136608591,1079529611,

%T 8530826457,67413620993,532726379847,4209793089371,33267280400913,

%U 262889866978817,2077449112980255,16416740845208075,129730917736941417,1025179795159015841

%N Number of nonary sequences of length n such that no two consecutive terms have distance 4.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (8,1,-14).

%F For n>2, a(n) = 8*a(n-1) + a(n-2) - 14*a(n-3), a(0)=1, a(1)=9, a(2)=71, a(3)=561.

%F G.f.: (1 + x - 2 x^2 - 2 x^3)/(1 - 8 x - x^2 + 14 x^3).

%e For n=2 the a(2) = 81 - 10 = 71 sequences contain every combination except these ten: 04,40,15,51,26,62,37,73,48,84.

%t LinearRecurrence[{8, 1, -14}, {1, 9, 71, 561}, 40]

%o (Python)

%o def a(n):

%o     if n in [0, 1, 2, 3]:

%o         return [1, 9, 71, 561][n]

%o     return 8*a(n-1)+a(n-2)-14*a(n-3)

%Y Cf. A040000, A003945, A083318, A078057, A003946, A126358, A003946, A055099, A003947, A015448, A126473. A287804-A287819.

%K nonn,easy

%O 0,2

%A _David Nacin_, Jun 02 2017