OFFSET
0,6
COMMENTS
Here the weight of a lattice path is the area under the path and above the x-axis. T(n,k) also counts the number of integer compositions of (3*n) + (2*k) + 6 with adjacent differences in {-1,1}, first part 1, and last part 3.
LINKS
John Tyler Rascoe, Python program.
EXAMPLE
Triangle begins:
k=0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
n=0: 1;
n=1: 1, 1, 1;
n=2: 1, 2, 2, 2, 1, 1;
n=3: 1, 3, 4, 5, 4, 4, 3, 2, 1, 1;
n=4: 1, 4, 7, 10, 11, 11, 11, 9, 8, 6, 5, 3, 2, 1, 1;
...
T(1,0) = 1: (NENN).
T(2,1) = 2: (NNEENN) and (NENNEN).
T(3,2) = 4: (NENENNNE), (NENNENEN), (NNEENNEN), and (NNENEENN).
PROG
(Python) # see linked program
CROSSREFS
Cf. A227543 (paths of this kind from (0,0) to (n,n), offset 1 for (0,0) to (n,n+1)).
KEYWORD
nonn,easy,tabf
AUTHOR
John Tyler Rascoe, Aug 26 2024
STATUS
approved