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%I #14 Nov 16 2015 15:46:28
%S 0,0,0,0,0,1,2,7,16,38,82,175,362,736,1468,2885,5596,10736,20398,
%T 38423,71818,133307,245890,450970,822788,1493992,2700800,4862566,
%U 8721608,15588371,27770338,49320863,87344004,154263972,271765362,477622769,837519742,1465470968
%N Number of binary words of length n with exactly one occurrence of subword 010 and exactly two occurrences of subword 101.
%H Alois P. Heinz, <a href="/A260505/b260505.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (6,-13,10,6,-18,11,6,-10,2,3,-2,-1).
%F G.f.: -x^5*(2*x^2-x+1)*(x-1)^3/((x^2-x+1)^2*(x^2+x-1)^4).
%e a(5) = 1: 10101.
%e a(6) = 2: 101011, 110101.
%e a(7) = 7: 0101101, 0110101, 1010110, 1010111, 1011010, 1101011, 1110101.
%e a(8) = 16: 00101101, 00110101, 01011011, 01011101, 01101011, 01110101, 10101100, 10101110, 10101111, 10110100, 10111010, 11010110, 11010111, 11011010, 11101011, 11110101.
%e a(9) = 38: 000101101, 000110101, 001011011, ..., 111011010, 111101011, 111110101.
%e a(10) = 82: 0000101101, 0000110101, 0001011011, ..., 1111011010, 1111101011, 1111110101.
%p gf:= -x^5*(2*x^2-x+1)*(x-1)^3/((x^2-x+1)^2*(x^2+x-1)^4):
%p a:= n-> coeff(series(gf,x,n+1),x,n):
%p seq(a(n), n=0..40);
%Y Cf. A118430, A164146, A255386, A260668, A260697.
%K nonn,easy
%O 0,7
%A _Alois P. Heinz_, Nov 11 2015
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