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A306315 Number of binary words of length n such that the difference between the number of 1's and the number of 0's is in the interval [-2,3] for every prefix and in the interval [-3,2] for every suffix.

%I A306315 #12 Sep 17 2019 18:04:42
%S A306315 1,2,4,6,12,18,35,54,103,162,307,486,926,1458,2823,4374,8688,13122,
%T A306315 26962,39366,84285,118098,265147,354294,838625,1062882,2664636,
%U A306315 3188646,8499263,9565938,27197074,28697814,87261592,86093442,280596321,258280326,903916589
%N A306315 Number of binary words of length n such that the difference between the number of 1's and the number of 0's is in the interval [-2,3] for every prefix and in the interval [-3,2] for every suffix.
%H A306315 Alois P. Heinz, <a href="/A306315/b306315.txt">Table of n, a(n) for n = 0..3911</a>
%H A306315 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0,11,0,-46,0,90,0,-81,0,28,0,-3)
%F A306315 G.f.: -(2*x^11-18*x^9+9*x^8+48*x^7+3*x^6-44*x^5-14*x^4+16*x^3+7*x^2-2*x-1) / ((3*x^2-1) *(x^2+x-1) *(x^2-x-1) *(x^3-2*x^2-x+1) *(x^3+2*x^2-x-1)).
%e A306315 a(3) = 6: 001, 010, 011, 100, 101, 110.
%e A306315 a(4) = 12: 0010, 0011, 0100, 0101, 0110, 1000, 1001, 1010, 1011, 1100, 1101, 1110.
%e A306315 a(5) = 18: 00101, 00110, 01001, 01010, 01011, 01100, 01101, 01110, 10001, 10010, 10011, 10100, 10101, 10110, 11000, 11001, 11010, 11100.
%e A306315 a(6) = 35: 001010, 001011, 001100, 001101, 001110, 010010, 010011, 010100, 010101, 010110, 011000, 011001, 011010, 011100, 100010, 100011, 100100, 100101, 100110, 101000, 101001, 101010, 101011, 101100, 101101, 101110, 110001, 110010, 110011, 110100, 110101, 110110, 111000, 111001, 111010.
%t A306315 LinearRecurrence[{0,11,0,-46,0,90,0,-81,0,28,0,-3},{1,2,4,6,12,18,35,54,103,162,307,486},40] (* _Harvey P. Dale_, Sep 17 2019 *)
%Y A306315 Odd bisection gives A008776.
%Y A306315 Cf. A306293, A306306.
%K A306315 nonn,easy
%O A306315 0,2
%A A306315 _Alois P. Heinz_, Feb 06 2019