A104000 Square array T(r,m) read by antidiagonals: number of cyclically reduced words of length m in F_r.

2, 4, 2, 6, 12, 2, 8, 30, 28, 2, 10, 56, 126, 84, 2, 12, 90, 344, 630, 244, 2, 14, 132, 730, 2408, 3126, 732, 2, 16, 182, 1332, 6570, 16808, 15630, 2188, 2, 18, 240, 2198, 14652, 59050, 117656, 78126, 6564, 2, 20, 306, 3376, 28574, 161052, 531450

Offset

1,1

Links

Table of n, a(n) for n=1..51.

I. Rivin, Growth in free groups (and other stories)

Formula

T(r, m) = (2r-1)^m + 1 + (r-1)(1+(-1)^m).

Example

2,2,2,2,2,2,2,2,2,
4,12,28,84,244,732,2188,6564,19684,
6,30,126,630,3126,15630,78126,390630,1953126,
8,56,344,2408,16808,117656,823544,5764808,40353608,
10,90,730,6570,59050,531450,4782970,43046730,387420490,
12,132,1332,14652,161052,1771572,19487172,214358892,2357947692,
14,182,2198,28574,371294,4826822,62748518,815730734,10604499374,

Crossrefs

Sequence in context: A085190 A285702 A371064 * A199943 A335340 A013599

Adjacent sequences: A103997 A103998 A103999 * A104001 A104002 A104003

Keyword

nonn,tabl

Author

Ralf Stephan, Feb 26 2005

Status

approved