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A287829 Number of sequences over the alphabet {0,1,...,9} such that no two consecutive terms have distance 6. 0

%I

%S 1,10,92,848,7816,72040,663992,6120008,56408056,519912520,4792028792,

%T 44168084168,407096815096,3752207504200,34584061167992,

%U 318760965520328,2938016812018936,27079673239211080,249593092776937592,2300497181470860488,21203660818791619576

%N Number of sequences over the alphabet {0,1,...,9} such that no two consecutive terms have distance 6.

%C In general, the number of sequences over the alphabet {0,1,...,9} such that no two consecutive terms have distance 5+k for k in {0,1,2,3,4} is given by a(n) = 9*a(n-1) + 2*k*a(n-2), a(0)=1, a(1)=10.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (9, 2).

%F a(n) = 9*a(n-1) + 2*a(n-2), a(0)=1, a(1)=10.

%F G.f.: (-1 - x)/(-1 + 9*x + 2*x^2).

%F a(n) = ((1 - 11/sqrt(89))/2)*((9 - sqrt(89))/2)^n + ((1 + 11/sqrt(89))/2)*((9 + sqrt(89))/2)^n.

%F a(n) = A015579(n)+A015579(n+1). - _R. J. Mathar_, Oct 20 2019

%t LinearRecurrence[{9, 2}, {1, 10}, 30]

%o (Python)

%o def a(n):

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

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

%o .return 9*a(n-1)+2*a(n-2)

%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

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Last modified March 2 05:06 EST 2021. Contains 341741 sequences. (Running on oeis4.)