OFFSET
1,3
COMMENTS
If the row is achiral, i.e., the same as its reverse, we ignore it. If different from its reverse, we count it and its reverse as a chiral pair.
LINKS
FORMULA
a(n) = (k!/2) * (S2(n,k) - S2(ceiling(n/2),k)), with k=3 colors used and where S2(n,k) is the Stirling subset number A008277.
G.f.: -(k!/2) * (x^(2k-1) + x^(2k)) / Product_{j=1..k} (1 - j*x^2) + (k!/2) * x^k / Product_{j=1..k} (1 - j*x) with k=3 colors used.
G.f.: 3*x^3*(5*x^2-x-1)/(-36*x^6+30*x^5+24*x^4-25*x^3-x^2+5*x-1). - Simon Plouffe, Jun 20 2018
EXAMPLE
For a(3) = 3, the chiral pairs are ABC-CBA, ACB-BCA, and BAC-CAB.
MATHEMATICA
k=3; Table[(k!/2) (StirlingS2[n, k] - StirlingS2[Ceiling[n/2], k]), {n, 1, 40}]
PROG
(PARI) a(n) = 3*(stirling(n, 3, 2)-stirling(ceil(n/2), 3, 2)); \\ Altug Alkan, Sep 26 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robert A. Russell, Jun 06 2018
STATUS
approved