OFFSET
0,2
COMMENTS
The given recurrences do not provide a means to calculate T(2r,r). But T(2r,r) is computable by the formula relating T(k,r) to A069466(k,r).
FORMULA
EXAMPLE
T(3,1)=84 because there are 84 distinct lattice walks of length 2*3=6 starting and ending at the origin and containing exactly 1 step to the east and not touching origin at intermediate steps. Let E, W, S, N denote the 4 possible directions, then NNEWSS and NWSSNE are examples of such walks.
MATHEMATICA
A069466[k_, r_] := Binomial[2 k, k]*Binomial[k, r]^2; t[k_, r_] := t[k, r] = A069466[k, r] - Sum[Sum[t[i, j]*A069466[k - i, r - j], {j, 0, r}], {i, 1, k - 1}]; Table[t[k, r], {k, 0, 8}, {r, 0, k}] // Flatten (* Jean-François Alcover, Nov 21 2012, from formula *)
CROSSREFS
KEYWORD
AUTHOR
Martin Wohlgemuth, Mar 24 2002
STATUS
approved