OFFSET
2,2
COMMENTS
a(n-1), n>=5, gives the number of necklaces with n beads (C_n symmetry) with color signature determined from the partition 2^2,1^(n-4) of n. Only n-2 distinct colors, say c[1], c[2], ..., c[n-2] are used, and the representative necklaces have the color c[1] and c[2] each twice. E.g., n=5, partition 2,2,1, color signature (take the parts as exponents) c[1]c[1]c[2]c[2]c[3], with the a(4)=6 necklaces (write j for color c[j]) 11223, 11232, 11322, 12213, 12123 and 12132, all taken cyclically. See A212359 for the numbers for general partitions or color signatures. - Wolfdieter Lang, Jun 27 2012
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 2..200
FORMULA
a(n) = numerator(n!/(2*(n! - 2))) for n > 2. - Stefano Spezia, Dec 06 2023
MATHEMATICA
Join[{1, 3}, Range[4, 30]!/4] (* Harvey P. Dale, Aug 13 2013 *)
PROG
(PARI) concat([1, 3], vector(66, n, (n+3)!/4)) \\ Joerg Arndt, Aug 14 2013
(Magma) [n le 3 select 2*n-3 else Factorial(n)/4: n in [2..30]]; // G. C. Greubel, Sep 28 2024
(SageMath)
def A133799(n): return (factorial(n) +2*int(n==2) +6*int(n==3))//4
[A133799(n) for n in range(2, 31)] # G. C. Greubel, Sep 28 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 17 2008
EXTENSIONS
Corrected parameters in definition. - Geoffrey Critzer, Apr 26 2009
STATUS
approved