A287826 - OEIS

%I #8 Jun 07 2017 13:08:10

%S 1,10,84,708,5968,50308,424080,3574860,30134944,254028100,2141377008,

%T 18051134892,152165391616,1282706408548,10812811724688,91148603152524,

%U 768354066287200,6476983198439812,54598931916359472,460251829451302764,3879778213203474880

%N Number of sequences over the alphabet {0,1,...,9} such that no two consecutive terms have distance 2.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (10, -13, -2).

%F a(n) = 10*a(n-1) - 13*a(n-2) - 2a(n-3), a(0)=1, a(1)=10, a(2)=84.

%F G.f.: (1 - 3 x^2)/(1 - 10 x + 13 x^2 + 2 x^3).

%t LinearRecurrence[{10, -13, -2}, {1, 10, 84}, 40]

%o (Python)

%o def a(n):

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

%o ..return [1, 10, 84][n]

%o .return 10*a(n-1)-13*a(n-2)-2*a(n-3)

%Y Cf. A040000, A003945, A083318, A078057, A003946, A126358, A003946, A055099, A003947, A015448, A126473. A287804-A287819. A287825-A287831.

%K nonn,easy

%O 0,2

%A _David Nacin_, Jun 02 2017