A076261 - OEIS

A076261

Triangle T(n,k) (n >= 2, 1 <= k <= n-1) read by rows, where T(n,k) is the number of words of length n in the free group on two generators that require exactly k multiplications for their formation.

4, 0, 8, 0, 4, 12, 0, 0, 18, 14, 0, 0, 10, 44, 10, 0, 0, 0, 50, 74, 4, 0, 0, 4, 38, 134, 80, 0, 0, 0, 0, 24, 184, 248, 56, 0, 0, 0, 0, 20, 198, 502, 288, 16, 0, 0, 0, 0, 0, 184, 686, 970, 208, 0, 0, 0, 0, 0, 10, 94, 1034, 1698, 1206, 54, 0, 0, 0, 0, 0, 0, 102, 860, 3170, 3226, 834, 0, 0, 0

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OFFSET

2,1

LINKS

Table of n, a(n) for n=2..79.

Sean A. Irvine, Java program (github)

EXAMPLE

T(4,2)=4 because we can generate each of aaaa, abab, baba, bbbb with just two multiplications: e.g., ab=a*b, abab=ab*ab.

From Sean A. Irvine, Mar 28 2025: (Start)

Triangle begins:

0, 8;

0, 4, 12;