|
Search: id:A124812
|
|
|
| A124812 |
|
Number of 4-ary Lyndon words of length n with exactly four 1s. |
|
+0
5
|
|
| 3, 21, 135, 702, 3402, 15282, 65610, 270540, 1082565, 4221639, 16120377, 60450138, 223205220, 813100356, 2927177028, 10428053400, 36804946455, 128817263385, 447470664795, 1543773631158, 5292938720718, 18044108743734, 61193066237550
(list; graph; listen)
|
|
|
OFFSET
|
5,1
|
|
|
FORMULA
|
o.g.f. 3 x^5 (1-5 x + 9 x^2 - 6 x^3)/((1-3 x^2)^2 (1- 3 x)^4) = 1/4*((x/(1-3*x))^4 - x^4/(1-3*x^2)^2) a(n) = 1/4*sum_{d|4,d|n} mu(d) C(n/d-1,(n-4)/d )*3^((n-4)/d) = 1/4*C(n-1,3)*3^(n-4) if n is odd = 1/4*C(n-1,3)*3^(n-4) - 1/4*(n/2-1)*3^((n-4)/2) if n is even
|
|
EXAMPLE
|
a(6) = 21 because 1111ab, 1111ba, 111a1b, 111b1a, 11a11b for ab = 23, 24, 34 (accounting for 15 words) and 1111aa, 111a1a for a=2,3,4 (accounting for 6 words) are all Lyndon of length 6
|
|
CROSSREFS
|
Cf. A124810, A124811, A124813, A124814, A006918, A124722.
Sequence in context: A121447 A125682 A125701 this_sequence A141041 A079753 A137969
Adjacent sequences: A124809 A124810 A124811 this_sequence A124813 A124814 A124815
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Mike Zabrocki (zabrocki(AT)mathstat.yorku.ca), Nov 08 2006
|
|
|
Search completed in 0.002 seconds
|
