cp's OEIS Frontend

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.

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A075099 Minimal total number of multiplications needed to generate all words of length n in the free monoid on two generators.

Original entry on oeis.org

0, 4, 11, 20, 42, 75
Offset: 1

Views

Author

Colin Mallows, Aug 31 2002

Keywords

Comments

Benoit Jubin (Jan 24 2009) suggests replacing "monoid" in the definition by "semigroup".
I believe a(2n) = a(n) + 2^(2n). I guess a(7) = 156.

Examples

			a(3)=11 because each of xxx,xxy,xyx,xyy,yxx,yxy,yyx,yyy can be obtained in one step from xx,xy,yy and it takes three multiplications to produce xx, xy, yy.

Crossrefs

Cf. A075100, A124677 (another version).

A075100 Number of words of length strictly between 1 and n that are needed on the way to computing all words of length n in the free monoid with two generators.

Original entry on oeis.org

0, 0, 3, 4, 10, 11
Offset: 1

Views

Author

Colin Mallows, Aug 31 2002

Keywords

Comments

I believe a(2n) = a(n) + 2^n. I think a(7) = 28.
Benoit Jubin (Jan 24 2009) suggests replacing "monoid" in the definition by "semigroup" and remarks that it makes sense to introduce a new sequence that includes words of length 1 in the count.

Examples

			a(3) = 3 because we need only xx, xy, yy to generate each of xxx, xxy, xyx, yxx, xyy, yxy, yyx, yyy.

Crossrefs

Cf. A075099, A003313, A124677.

Extensions

Edited by Andrey Zabolotskiy, Nov 08 2024
Showing 1-2 of 2 results.

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