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A255386 Number of binary words of length n with exactly one occurrence of subword 010 and exactly one occurrence of subword 101. 6

%I

%S 0,0,0,0,2,4,10,20,42,84,166,320,608,1140,2116,3892,7102,12868,23170,

%T 41488,73918,131104,231578,407520,714672,1249368,2177736,3785688,

%U 6564362,11355940,19602154,33767228,58056786,99638364,170711134,292011872,498747632

%N Number of binary words of length n with exactly one occurrence of subword 010 and exactly one occurrence of subword 101.

%H Alois P. Heinz, <a href="/A255386/b255386.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4,-2,5,-2,-2,2,1).

%F G.f.: -2*x^4*(x-1)^2/((x^2-x+1)*(x^2+x-1)^3).

%e a(4) = 2: 0101, 1010.

%e a(5) = 4: 00101, 01011, 10100, 11010.

%e a(6) = 10: 000101, 001011, 010110, 010111, 011010, 100101, 101000, 101001, 110100, 111010.

%e a(8) = 42: 00000101, 00001011, 00010110, 00010111, 00011010, 00101100, 00101110, 00101111, 00110100, 00111010, 01001101, 01011000, 01011001, 01011100, 01011110, 01011111, 01100101, 01101000, 01101001, 01110100, 01111010, 10000101, 10001011, 10010110, 10010111, 10011010, 10100000, 10100001, 10100011, 10100110, 10100111, 10110010, 11000101, 11001011, 11010000, 11010001, 11010011, 11100101, 11101000, 11101001, 11110100, 11111010.

%p a:= n-> coeff(series(-2*x^4*(x-1)^2/

%p ((x^2-x+1)*(x^2+x-1)^3), x, n+1), x, n):

%p seq(a(n), n=0..50);

%t LinearRecurrence[{4,-4,-2,5,-2,-2,2,1},{0,0,0,0,2,4,10,20},40] (* _Harvey P. Dale_, Apr 09 2016 *)

%Y Cf. A118430, A260697.

%K nonn

%O 0,5

%A _Alois P. Heinz_, May 05 2015

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Last modified August 13 22:57 EDT 2020. Contains 336473 sequences. (Running on oeis4.)