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

1, 1, 1, 3, 7, 14, 26, 47, 86, 160, 300, 562, 1051, 1962, 3661, 6833, 12757, 23820, 44477, 83045, 155052, 289493, 540506, 1009172, 1884217, 3518007, 6568439, 12263866, 22897737, 42752130, 79822071, 149034991, 278261743, 519539714, 970027388, 1811128400

Offset: 0

Author

Alois P. Heinz, Aug 08 2018

Keywords

• nonn
• easy

Comments

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.

Examples

			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.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..2000
• Index entries for linear recurrences with constant coefficients, signature (1,1,1,0,0,1,1,-1,-1,-1).

Crossrefs

Cf. A000045, A317669, A317783.

Programs

Maple

a:= n-> coeff(series((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),x,n+1),x,n):
seq(a(n), n=0..35);

Formula

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).