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%I #9 Jun 05 2017 16:02:21
%S 1,7,41,241,1417,8333,49005,288193,1694833,9967141,58615749,344713305,
%T 2027224169,11921900829,70111496093,412318635697,2424804301985,
%U 14260029486677,83861794865077,493182755657289,2900358033942041,17056713010658765,100308808541321741
%N Number of septenary sequences of length n such that no two consecutive terms have distance 3.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6, 1, -10).
%F For n>3, a(n) = 6*a(n-1) + a(n-2) - 10*a(n-3), a(0)=1, a(1)=7, a(2)=41, a(3)=241.
%F G.f.: (1 + x - 2*x^2 - 2*x^3)/(1 - 6*x - x^2 + 10*x^3).
%e For n=2 the a(2) = 49-8 = 41 sequences contain every combination except these eight: 03, 30, 14, 41, 25, 52, 36, 63.
%t LinearRecurrence[{6, 1, -10}, {1, 7, 41, 241}, 40]
%o (Python)
%o def a(n):
%o .if n in [0, 1, 2, 3]:
%o ..return [1, 7, 41, 241][n]
%o .return 6*a(n-1)+a(n-2)-10*a(n-3)
%Y Cf. A040000, A003945, A083318, A078057, A003946, A126358, A003946, A055099, A003947, A015448, A126473.
%Y Cf. A287804-A287819.
%K nonn,easy
%O 0,2
%A _David Nacin_, Jun 01 2017