OFFSET
1,5
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.
FORMULA
a(n) = (k!/2) * (S2(n,k) - S2(ceiling(n/2),k)), with k=5 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=5 colors used.
EXAMPLE
For a(5) = 60, the chiral pairs are the 5! = 120 permutations of ABCDE, each paired with its reverse.
MATHEMATICA
k=5; Table[(k!/2) (StirlingS2[n, k] - StirlingS2[Ceiling[n/2], k]), {n, 1, 40}]
PROG
(PARI) a(n) = 60*(stirling(n, 5, 2) - stirling(ceil(n/2), 5, 2)); \\ Altug Alkan, Sep 26 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robert A. Russell, Jun 06 2018
STATUS
approved