OFFSET
1,2
COMMENTS
Let a meander be defined as in the link and m = 3. Then T(n,k) counts the invertible meanders of length m(n+1) built from arcs with central angle 360/m whose binary representation have mk '1's.
LINKS
Peter Luschny, Meanders.
EXAMPLE
[1] 1
[2] 4, 4
[3] 9, 36, 9
[4] 16, 168, 168, 16
[5] 25, 550, 1400, 550, 25
[6] 36, 1440, 7500, 7500, 1440, 36
T(2,1) = 4 because the invertible meanders of length 9 and central angle 120 degree which have three '1's in their binary representation are {100100100, 100011000, 110001000, 111000000}.
MAPLE
MATHEMATICA
t[n_, k_] := k*Binomial[n, k]^3*(n^2 + n - k*n - k + k^2)/((n - k + 1)^2*n); Table[t[n, k], {n, 1, 9}, {k, 1, n}] // Flatten (* Jean-François Alcover, Jul 02 2013 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny and Susanne Wienand, Dec 19 2011
STATUS
approved