This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A260505 #16 Jun 26 2025 15:22:36
%S A260505 0,0,0,0,0,1,2,7,16,38,82,175,362,736,1468,2885,5596,10736,20398,
%T A260505 38423,71818,133307,245890,450970,822788,1493992,2700800,4862566,
%U A260505 8721608,15588371,27770338,49320863,87344004,154263972,271765362,477622769,837519742,1465470968
%N A260505 Number of binary words of length n with exactly one occurrence of subword 010 and exactly two occurrences of subword 101.
%H A260505 Alois P. Heinz, <a href="/A260505/b260505.txt">Table of n, a(n) for n = 0..1000</a>
%H A260505 <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 A260505 G.f.: -x^5*(2*x^2-x+1)*(x-1)^3/((x^2-x+1)^2*(x^2+x-1)^4).
%e A260505 a(5) = 1: 10101.
%e A260505 a(6) = 2: 101011, 110101.
%e A260505 a(7) = 7: 0101101, 0110101, 1010110, 1010111, 1011010, 1101011, 1110101.
%e A260505 a(8) = 16: 00101101, 00110101, 01011011, 01011101, 01101011, 01110101, 10101100, 10101110, 10101111, 10110100, 10111010, 11010110, 11010111, 11011010, 11101011, 11110101.
%e A260505 a(9) = 38: 000101101, 000110101, 001011011, ..., 111011010, 111101011, 111110101.
%e A260505 a(10) = 82: 0000101101, 0000110101, 0001011011, ..., 1111011010, 1111101011, 1111110101.
%p A260505 gf:= -x^5*(2*x^2-x+1)*(x-1)^3/((x^2-x+1)^2*(x^2+x-1)^4):
%p A260505 a:= n-> coeff(series(gf,x,n+1),x,n):
%p A260505 seq(a(n), n=0..40);
%t A260505 LinearRecurrence[{6,-13,10,6,-18,11,6,-10,2,3,-2,-1},{0,0,0,0,0,1,2,7,16,38,82,175},40] (* _Harvey P. Dale_, Jun 26 2025 *)
%Y A260505 Cf. A118430, A164146, A255386, A260668, A260697.
%K A260505 nonn,easy
%O A260505 0,7
%A A260505 _Alois P. Heinz_, Nov 11 2015