A047140 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.).

1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 2, 4, 4, 1, 1, 3, 2, 8, 5, 1, 1, 4, 5, 10, 13, 6, 1, 1, 5, 9, 15, 23, 19, 7, 1, 1, 6, 14, 24, 38, 42, 26, 8, 1, 1, 7, 20, 38, 62, 80, 68, 34, 9, 1, 1, 8, 27, 58, 38, 142, 148, 102, 43, 10, 1, 1, 9, 35, 85, 96, 180, 290

Offset

0,5

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1325

Example

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 ...
  ...

Prog

(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

Crossrefs

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

Cf. A047110, A047130, A047150.

Sequence in context: A111603 A180178 A136178 * A047150 A280489 A289356

Adjacent sequences: A047137 A047138 A047139 * A047141 A047142 A047143

Keyword

nonn,tabl

Author

Clark Kimberling. Definition revised Dec 08 2006

Status

approved