A047130 Array read by descending antidiagonals: T(h,k) is the 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 = 3x/4. (Thus a path crosses the line only at lattice points and on right-steps.)

1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 3, 2, 3, 1, 1, 4, 5, 5, 4, 1, 1, 5, 9, 5, 9, 5, 1, 1, 6, 14, 14, 14, 14, 6, 1, 1, 7, 20, 28, 28, 28, 20, 7, 1, 1, 8, 27, 48, 56, 28, 48, 27, 8, 1, 1, 9, 35, 75, 104, 84, 76, 75, 35, 9, 1, 1, 10, 44, 110, 179, 188, 84

Offset

0,8

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 1  2  3   4   5   6   7 ...
  2 | 1 2  2  5   9  14  20  27 ...
  3 | 1 3  5  5  14  28  48  75 ...
  4 | 1 4  9 14  28  56 104 179 ...
  5 | 1 5 14 28  28  84 188 367 ...
  6 | 1 6 20 48  76  84 272 639 ...
  7 | 1 7 27 75 151 235 272 911 ...
  ...

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(4*k>3*h && 4*(k-1)<3*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. A047131, A047132, A047133, A047134, A047135, A047136, A047137, A047138, A047139.

Cf. A047110, A047140, A047150.

Sequence in context: A057555 A075532 A050176 * A125778 A047110 A288533

Adjacent sequences: A047127 A047128 A047129 * A047131 A047132 A047133

Keyword

nonn,tabl

Author

Clark Kimberling. Definition revised Dec 08 2006

Status

approved