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A317779 Number of equivalence classes of binary words of length n for the set of subwords {010, 101, 10110}. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

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 all each single subword.

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).

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).

EXAMPLE

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.

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);

CROSSREFS

Cf. A000045, A317669, A317783.

Sequence in context: A293767 A014168 A132109 * A099854 A054355 A245268

Adjacent sequences:  A317776 A317777 A317778 * A317780 A317781 A317782

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Aug 08 2018

STATUS

approved

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Last modified May 19 21:29 EDT 2019. Contains 323410 sequences. (Running on oeis4.)