OFFSET
0,2
LINKS
J. Brawner, Three-Dimensional Lattice Walks in the Upper Half-Space: Problem 10795, Amer. Math. Monthly, 108 (Dec. 2001), 980.
FORMULA
T(n, k) = binomial(n, k)*binomial(k, ceiling(k/2))*4^(n-k).
EXAMPLE
T(2,1)=8 because we have NU, SU, EU, WU, UN, US, UE and UW, where N=(0,1,0),S=(0,-1,0), E=(1,0,0),W=(-1,0,0), U=(0,0,1) and S=(0,0,-1).
Triangle begins:
1;
4, 1;
16, 8, 2;
64, 48, 24, 3;
MAPLE
T:=(n, k)->binomial(n, k)*binomial(k, ceil(k/2))*4^(n-k): for n from 0 to 9 do seq(T(n, k), k=0..n) od; # yields sequence in triangular form
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Emeric Deutsch, Apr 23 2005
STATUS
approved