cp's OEIS Frontend

A317779 Number of equivalence classes of binary words of length n for the set of subwords {010, 101, 10110}.

%I A317779 #25 Aug 16 2020 10:14:59
%S A317779 1,1,1,3,7,14,26,47,86,160,300,562,1051,1962,3661,6833,12757,23820,
%T A317779 44477,83045,155052,289493,540506,1009172,1884217,3518007,6568439,
%U A317779 12263866,22897737,42752130,79822071,149034991,278261743,519539714,970027388,1811128400
%N A317779 Number of equivalence classes of binary words of length n for the set of subwords {010, 101, 10110}.
%C A317779 Two binary words of the same length are equivalent with respect to a given subword set if they have equal sets of occurrences for each single subword.
%H A317779 Alois P. Heinz, <a href="/A317779/b317779.txt">Table of n, a(n) for n = 0..2000</a>
%H A317779 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1,0,0,1,1,-1,-1,-1).
%F A317779 G.f.: (x^9+2*x^8+2*x^7-x^6-3*x^5-2*x^4+x^2-1)/(-x^10-x^9-x^8+x^7+x^6+x^3+x^2+x-1).
%e A317779 a(7) = 47: [||], [|0|], [0||], [|1|], [|2|], [|3|], [|4|], [1||], [2||], [3||], [4||], [|0|0], [|04|], [03||], [04||], [14||], [1|0|], [0|1|], [2|1|], [1|2|], [3|2|], [2|3|], [4|3|], [3|4|], [|1|1], [|2|2], [02|1|], [1|02|], [13|2|], [2|13|], [14|0|], [24|3|], [03|4|], [3|24|], [|03|0], [|14|1], [0|1|1], [1|2|2], [13|02|], [02|13|], [24|13|], [13|24|], [1|02|2], [4|03|0], [0|14|1], [024|13|], [13|024|].  Here [1|02|2] describes the class whose members have an occurrence of 010 at position 1 and occurrences of 101 at positions 0 and 2 and an occurrence of 10110 at position 2 and no other occurrences of the subwords: 1010110.
%p A317779 a:= n-> coeff(series((x^9+2*x^8+2*x^7-x^6-3*x^5-2*x^4+x^2-1)/
%p A317779              (-x^10-x^9-x^8+x^7+x^6+x^3+x^2+x-1),x,n+1),x,n):
%p A317779 seq(a(n), n=0..35);
%Y A317779 Cf. A000045, A317669, A317783.
%K A317779 nonn,easy
%O A317779 0,4
%A A317779 _Alois P. Heinz_, Aug 08 2018