OFFSET
0,5
LINKS
Alois P. Heinz, Antidiagonals n = 0..140, flattened
M. Dziemianczuk, Counting Lattice Paths With Four Types of Steps, Graphs and Combinatorics, September 2013, Volume 30, Issue 6, pp 1427-1452.
FORMULA
Dziemianczuk gives a g.f.
EXAMPLE
Array begins:
1,1,1,1,1,1,1,1,1,...
1,4,12,36,108,324,972,2916,8748,...
1,7,33,143,609,2583,10945,46367,196417,...
1,10,63,341,1748,8773,43653,216434,1071483,...
1,13,102,656,3860,21756,119948,653612,3539052,...
1,16,150,1115,7376,45801,274243,1606727,9288000,...
1,19,207,1745,12809,86739,558967,3489601,21333553,...
...
MAPLE
b:= proc(x, y, m) option remember; `if`(x=0 and y=0, 1,
`if`(x>0, b(x-1, y, m), 0)+`if`(y>0, b(x, y-1, m), 0)+
`if`(x>0 and y>0, b(x-1, y-1, m), 0)+
`if`(x<m and y>0, b(x+1, y-1, m), 0))
end:
T:= (n, k)-> b(n, k, n):
seq(seq(T(d-k, k), k=0..d), d=0..12); # Alois P. Heinz, Apr 03 2014
MATHEMATICA
b[x_, y_, m_] := b[x, y, m] = If[x == 0 && y == 0, 1, If[x>0, b[x-1, y, m], 0] + If[y>0, b[x, y-1, m], 0] + If[x>0 && y>0, b[x-1, y-1, m], 0] + If[x<m && y>0, b[x+1, y-1, m], 0]]; T[n_, k_] := b[n, k, n]; Table[Table[T[d-k, k], {k, 0, d}], {d, 0, 12}] // Flatten (* Jean-François Alcover, Apr 24 2014, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Dec 05 2013
EXTENSIONS
More terms from Alois P. Heinz, Apr 03 2014
STATUS
approved