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Number of length n binary sequences with at most 4 of every adjacent 6 bits set.
0

%I #10 Aug 14 2023 18:20:45

%S 1,2,4,8,16,31,57,109,209,401,769,1473,2817,5391,10321,19761,37834,

%T 72432,138663,265455,508195,972909,1862575,3565778,6826437,13068741,

%U 25019217,47897608,91696751,175547250,336073354,643389727,1231726180

%N Number of length n binary sequences with at most 4 of every adjacent 6 bits set.

%H <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, 1, 0, 1, 2, 0, -2, -2, 0, 0, -1, 0, 0, 1).

%F Conjectures from _Colin Barker_, Feb 22 2018: (Start)

%F G.f.: (1 + x + x^2 + x^3 + 2*x^4 + 2*x^5 - 2*x^6 - 3*x^7 - 2*x^8 - x^10 - x^11 + x^13 + x^14) / (1 - x - x^2 - x^3 - x^5 - 2*x^6 + 2*x^8 + 2*x^9 + x^12 - x^15).

%F a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-5) + 2*a(n-6) - 2*a(n-8) - 2*a(n-9) - a(n-12) + a(n-15) for n>14.

%F (End)

%t CoefficientList[Series[(1+x+x^2+x^3+2x^4+2x^5-2x^6-3x^7-2x^8-x^10-x^11+x^13+x^14)/(1-x-x^2-x^3-x^5-2x^6+2x^8+2x^9+x^12-x^15),{x,0,50}],x] (* or *) LinearRecurrence[ {1,1,1,0,1,2,0,-2,-2,0,0,-1,0,0,1},{1,2,4,8,16,31,57,109,209,401,769,1473,2817,5391,10321},50] (* _Harvey P. Dale_, Aug 14 2023 *)

%K nonn

%O 0,2

%A _R. H. Hardin_, Dec 24 2007