proposed

approved

editing

proposed

Andrew Howroyd, <a href="/A047140/b047140.txt">Table of n, a(n) for n = 0..1325</a>

Array begins:

======================================

h\k | 0 1 2 3 4 5 6 7

----+---------------------------------

0 | 1 1 1 1 1 1 1 1 ...

1 | 1 2 1 2 3 4 5 6 ...

2 | 1 3 4 2 5 9 14 20 ...

3 | 1 4 8 10 15 24 38 58 ...

4 | 1 5 13 23 38 62 38 96 ...

5 | 1 6 19 42 80 142 180 96 ...

6 | 1 7 26 68 148 290 470 566 ...

7 | 1 8 34 102 250 540 1010 1576 ...

...

(PARI) A(h, k=h)={my(M=matrix(h+1, k+1, i, j, 1)); for(h=1, h, for(k=1, k, M[1+h, 1+k] = M[h, 1+k] + if(3*k>4*h && 3*(k-1)<4*h, 0, M[1+h, k]))); M}

{ my(T=A(10)); for(i=1, #T, print(T[i, ]))} \\ Andrew Howroyd, Jan 19 2020

Cf. A047141, A047142, A047143, A047144, A047145, A047146, A047147, A047148, A047149.

Cf. A047110, A047130, A047150.

approved

editing

_Clark Kimberling (ck6(AT)evansville.edu)_. Definition revised Dec 08 2006

Array read by diagonals: T(h,k)=number of paths consisting of steps from (0,0) to (h,k) such that each step has length 1 directed up or right, and no up-step crosses the line y=4x/3. (Thus a path crosses the line only at lattice points and on right-steps.).

nonn,tabl,new

Array T read by diagonals: T(h,k)=number of paths consisting of steps from (0,0) to (h,k) such that each step has length 1 directed up or right , and touches no up-step crosses the line y=4x/3 . (Thus a path crosses the line only at lattice points and on right-steps.).

nonn,tabl,new

Clark Kimberling (ck6(AT)evansville.edu). Definition revised Dec 08 2006

Array T read by diagonals: T(h,k)=number of paths consisting of steps from (0,0) to (h,k) such that each step has length 1 directed up or right and touches the line y=4x/3 only at lattice points.

nonn,tabl,new

nonn,tabl,new

Clark Kimberling, (ck6(AT)evansville.edu)

nonn,tabl,new

Clark Kimberling, ck6@cedar.(AT)evansville.edu